analysis of hydraulic tomography using temporal moments of drawdown recovery data received 2 june 2005 revised 30 september 2005 accepted 21 october 2005 published 1 february 2006 1 transient hydraulic tomography tht is a potentially cost effective and highresolution technique for mapping spatial distributions of the hydraulic conductivity and specific storage in aquifers interpretation of abundant well hydrographs of a tht survey however is a computational challenge we take on this challenge by developing an estimation approach that utilizes the zeroth and first temporal moments of well hydrographs instead of drawdown itself the governing equations for the temporal moments are poisson s equations these equations demand less computational resources as opposed to the parabolic equation that governs drawdown evolution likewise the adjoint equations for evaluating sensitivities of the moments for parameter estimation also take the same forms therefore a temporal moment approach is expected to expedite the interpretation of tht surveys on the basis of this premise we extend our sequential successive linear estimator to use the zeroth moment and characteristic time of the drawdown recovery data generated by tht surveys we subsequently investigate computational efficiency and accuracy of the moment approach results of the investigation show that the temporal moment approach yields results similar to those from the approach that uses transient heads but at significantly less computational costs limitations using temporal moments are discussed subsequently

solutions of nonlinear dirac equations abstract we study the dirac equation i t i c k 1 3 k k m c 2 g x and obtain existence and multiplicity results of stationary solutions for several classes of nonlinearities g r 3 c 4 r modeling various types of interaction a typical result states that if g x u depends periodically on x and is even in u the problem has infinitely many geometrically different localized solutions the arguments are variational the associated lagrangian functional is strongly indefinite and the palais smale condition does not hold we apply some recently developed critical point theorems

homoclinic orbits on compact hypersufaces in 293 1293 1293 1 of restricted contact type consider a smooth hamiltonian system in 2n dot x jh x the energy surface x h x h 0 being compact and 0 being a hyperbolic equilibrium we assume moreover that 0 is of restricted contact type these conditions are symplectically invariant by a variational method we prove the existence of an orbit homoclinic i e non constant and doubly asymptotic to 0

existence and multiplicity of solutions for asymptotically hamiltonian elliptic systems in rn abstract this paper is concerned with the following nonperiodic hamiltonian elliptic system u v x u h u x u v in r n v v x v h v x u v in r n u x 0 and v x 0 as x where the potential v is bounded below and h is asymptotically linear in z as z with z u v by applying a generalized linking theorem of strongly indefinite functionals we obtain solutions for the above system

homoclinic orbits and periodic solutions for a class of hamiltonian systems on time scales abstract in this paper we are concerned with a second order non autonomous hamiltonian system on time scales t u t v u t u t f t t t under certain conditions the existence and multiplicity of periodic solutions are obtained for this hamiltonian system on time scales by using the saddle point theory the least action principle as well as the three critical point theorem in addition the existence of homoclinic orbit is obtained as a limit of 2 k t periodic solutions of a given sequence of hamiltonian system on time scales by means of the mountain pass theorem and the standard minimizing argument

existence and multiplicity of homoclinic orbits for potentials on unbounded domains we study the system in r n where v is a potential with a strict local maximum at 0 and possibly with a singularity first using a minimising argument we can prove the existence of a homoclinic orbit when the component of x r n v x containing 0 is an arbitrary open set in the case unbounded we allow v x to go to 0 at infinity although at a slow enough rate then we show that the presence of a singularity in implies that a homoclinic solution can also be found via a minimax procedure and comparing the critical levels of the functional associated to the system we see that the two solutions are distinct whenever the singularity is not too far from 0

homoclinic orbits for a class of first order nonperiodic asymptotically quadratic hamiltonian systems with spectrum point zero in this paper we study the existence and multiplicity of homoclinic orbits for a class of first order nonperiodic hamiltonian systems by applying two recent critical point theorems for strongly indefinite functionals we give some new criteria to guarantee that hamiltonian systems with asymptotically quadratic terms and spectrum point zero have at least one and a finite number of pairs of homoclinic orbits under some adequate conditions respectively

on hamiltonian elliptic systems with periodic or non periodic potentials abstract this paper is concerned with the following hamiltonian elliptic system u b x u v x u h v x u v v b x v v x v h u x u v for x r n existence and multiplicity of solutions are obtained for the systems with periodic or non periodic potentials v via variational methods

a stochastic inverse solution for transient groundwater flow parameter identification and reliability analysis in this paper a stochastic approach is developed for solving the inverse problem of parameter identification for transient groundwater flow adjoint state equations are derived for the stochastic partial differential equation spde relating transient head and log hydraulic conductivity perturbations the derived equations can be used to calculate the covariance matrix of head observations and the cross covariance matrix between head observations and log hydraulic conductivity measurements for each observation time as well as the covariance and cross covariance matrices between different observation times the number of simulation runs required for obtaining these matrices is equal to the number of head observations the reliability of model prediction is evaluated through the variance estimate method using adjoint sensitivity analysis and the cokriging estimate the reliability evaluation of model prediction can be used as an aid in the optimization of experimental design for sampling strategies a numerical example is given to illustrate the stochastic inverse procedure for a general transient flow problem the example shows that using head observations of all observation times simultaneously produces much better results than using them sequentially commonly known as the quasi steady approach the example also shows that it is possible to obtain a reliable stochastic inverse solution for meeting a given prediction objective based on a limited number of observations

multiple solutions for a semiclassical schrodinger equation abstract this paper is concerned with the semiclassical nonlinear schrodinger equation e 2 u v x u f x u x r n u x 0 as x where e 0 is a small parameter under certain hypotheses on v and a general spectral assumption the existence and multiplicity of semiclassical solutions are obtained for asymptotically linear nonlinearity via variational methods

homoclinic orbits for second order self adjoint difference equations abstract in this paper we discuss how to use variational methods to study the existence of nontrivial homoclinic orbits of the following nonlinear difference equations p t u t 1 q t u t f t u t t z without any periodicity assumptions on p t q t and f providing that f t x grows superlinearly both at origin and at infinity or is an odd function with respect to x r and satisfies some additional assumptions

quasi linear geostatistical theory for inversing a quasi linear theory is presented for the geostatistical solution to the inverse problem the archetypal problem is to estimate the log transmissivity function from observations of head and log transmissivity at selected locations the unknown is parameterized as a realization of a random field and the estimation problem is solved in two phases structural analysis where the random field is characterized followed by estimation of the log transmissivity conditional on all observations the proposed method generalizes the linear approach of kitanidis and vomvoris 1983 the generalized method is superior to the linear method in cases of large contrast in formation properties but informative measurements i e there are enough observations that the variance of estimation error of the log transmissivity is small the methodology deals rigorously with unknown drift coefficients and yields estimates of covariance parameters that are unbiased and grid independent the applicability of the methodology is demonstrated through an example that includes structural analysis determination of best estimates and conditional simulations

the unregularized gradient flow of the symplectic action the symplectic action can be defined on the space of smooth paths in a symplectic manifold p which join two lagrangian submanifolds of p to pursue a new approach to the variational theory of this function we define on a subset of the path space the flow whose trajectories are given by the solutions of the cauchy riemann equation with respect to a suitable almost complex structure on p in particular we prove compactness and transversality results for the set of bounded trajectories

conditional stochastic analysis of solute transport in heterogeneous variably saturated soils a method is developed for the conditional monte carlo simulation of steady stateflow and transient transport from point sources in variably saturated porous media it combines the geostatistical method a linearized approximation of the soil water tension perturbation solution and afinite element numerical model the method is used to investigate the usefulness of conditional simulation for predicting solute transport under a variety of sampling network designs applied to a number of hypothetical soils saturated hydraulic conductivity data yield the largest reduction of conditional uncertainty in relatively wet soils with mild heterogeneities in highly heterogeneous soils or under dry conditions soil water tension data by themselves taken at a sampling density of one to two correlation scales along the expected mean travel path can greatly reduce prediction uncertainty about solute concentration parameter uncertainty about statistical properties of the independent random variables becomes less important as the number of conditioning data increases however even with a very high number of sampling data uncertainty of predicted concentration levels remains significant

existence of infinitely many homoclinic orbits for nonperiodic superquadratic hamiltonian systems abstract in this paper we study the following nonperiodic hamiltonian system z j h z t z where h t z is superquadratic in z r 2 n as z by applying a generalized linking theorem for strongly indefinite functionals we obtain infinitely many homoclinic orbits for the above system

numerical solutions of stochastic differential equations implementation and stability issues stochastic differential equations sdes arise from physical systems where the parameters describing the system can only be estimated or are subject to noise there has been much work done recently on developing numerical methods for solving sdes this paper will focus on stability issues and variable stepsize implementation techniques for numerically solving sdes effectively

coupled inverse problems in groundwater modeling 1 sensitivity analysis and parameter identification some basic concepts and methods for solving the coupled inverse problem in groundwater modeling are presented in a series of two papers because there are crossover effects between state variables and parmeters coupled inverse problems are different from single inverse problems in several aspects especially in the selection of objective functions identifiability and experimental design this paper discusses the general definition of coupled inverse problems posed in the framework of multiobjective optimization in order to obtain gradient vectors of objective functions as well as all sensitivity coefficients a general procedure for deriving the adjoint state equations and their associated conditions is described using the rules of adjoint operation presented in this paper the derivation of adjoint problems becomes very easy even for nonlinear and transient coupled problems as examples the adjoint problem of flow mass transport or flow heat transport the adjoint problem of saltwater intrusion and the adjoint problem of two phase flow are derived numerical experiments on a two dimensional flow mass transport problem are given to explain the procedure of sensitivity analysis and parameter identification for coupled problems the hydraulic conductivity can be identified by using observations of head and or solute concentration

on ground state solutions for some non autonomous schrodinger poisson systems abstract in this paper we study the schrodinger poisson system sp u u k x x u a x f u in r 3 k x u 2 in r 3 and prove the existence of ground state solutions for system sp under certain assumptions on the linear and nonlinear terms some recent results from different authors are extended

nonlinear inhomogeneous fokker planck equation within a generalized stratonovich prescription we deduce a nonlinear and inhomogeneous fokker planck equation within a generalized stratonovich or stochastic ensuremath alpha prescription ensuremath alpha 0 1 2 and 1 respectively correspond to the it o stratonovich and anti it o prescriptions we obtain its stationary state p st x for a class of constitutive relations between drift and diffusion and show that it has a q exponential form p st x n q 1 ensuremath 1 ensuremath q ensuremath beta v x 1 1 ensuremath q with an index q which does not depend on ensuremath alpha in the presence of any nonvanishing nonlinearity this is in contrast with the linear case for which the index q is ensuremath alpha dependent

morse theory for lagrangian intersections soit p une variete symplectique compacte et soit l p une sous variete lagrangienne avec 2 p l 0 pour un diffeomorphisme exact de p avec la propriete que l coupe l transversalement on demontre une inegalite de morse reliant l ensemble l l a la cohomologie de l

homoclinic solutions of hamiltonian systems with symmetry abstract we prove the existence of infinitely many homoclinic solutions for a first order hamiltonian system symmetric with respect to an action of a compact lie group by means of variational methods we make no convexity assumption on the hamiltonian

an application of the geostatistical approach to the inverse problem in two dimensional groundwater modeling the geostatistical approach to the estimation of transmissivity from head and transmissivity measurements is developed for two dimensional steady flow the field of the logarithm of transmissivity log transmissivity is represented as a zero order intrinsic random field its spatial structure is described in this application through a two term covariance function that is linear in the parameters 1 and 2 linearization of the discretized flow equations allows the construction of the joint covariance matrix of the head and log transmissivity measurements as a linear function of 1 and 2 in this particular application the coefficient matrices are calculated numerically in a noniterative fashion maximum likelihood estimation is employed to estimate 1 and 2 as well as additional parameters from measurements linear estimation theory cokriging then yields point or block averaged estimates of transmissivity the approach is first applied to a test case with favorable results it is shown that the application of the methodology gives good estimates of transmissivities it is also shown that when the transmissivities are used in a numerical model they reproduce the head measurements quite well results from the application of the methodology to the jordan aquifer in iowa are also presented

infinitely many homoclinic orbits for the second order hamiltonian systems with general potentials abstract in this paper we study the following nonperiodic second order hamiltonian systems u t l t u t r t u t r where l t may not be uniformly positive definite for all t r under more general conditions on r u t u we prove that the above system has infinitely many homoclinic orbits provided r is even in u

an inverse model for three dimensional flow in variably saturated porous media geostatistical theory has shown promise in dealing with issues of stability uniqueness and identity of estimates inherent in inverse problems of subsurface flow here the geostatistical method is extended to three dimensional unsteady flow in variably saturated porous geological media the vadose zone that are modeled using the richards equation and the van genuchten mualem constitutive equations the saturated hydraulic conductivity and n parameters of this relationship are treated as spatially correlated statistically independent stochastic processes for representing heterogeneity of porous media for given covariance functions of the parameters the adjoint state sensitivity method is used to calculate first order approximations for covariances of capillary pressure and moisture content and cross covariances between capillary pressure moisture content and the hydraulic properties these covariances and cross covariances are then used in a successive linear estimator sle to estimate the conditional means of the heterogeneous hydraulic property fields based on measurements of pressure and moisture content data a sequential conditioning approach for our sle was also applied to data sets collected at different sampling times during a transient infiltration event this approach has the benefit of reducing the size of the matrices and so helps avoid numerical stability problems on the basis of our study pressure and moisture content data sets collected at later times of an infiltration event or during steady state flow were found to provide better estimates smaller mean square error compared to the true field of the hydrological parameters of the vadose zone than data from very early times

analytical sensitivity analysis of transient groundwater flow in a bounded model domain using the adjoint method sensitivity analyses are an important component of any modeling exercise we have developed an analytical methodology based on the adjoint method to compute sensitivities of a state variable hydraulic head to model parameters hydraulic conductivity and storage coefficient for transient groundwater flow in a confined and randomly heterogeneous aquifer under ambient and pumping conditions for a special case of two dimensional rectangular domains these sensitivities are represented in terms of the problem configuration the domain size boundary configuration medium properties pumping schedules and rates and observation locations and times and there is no need to actually solve the adjoint equations as an example we present analyses of the obtained solution for typical groundwater flow conditions analytical solutions allow us to calculate sensitivities efficiently which can be useful for model based analyses such as parameter estimation data worth evaluation and optimal experimental design related to sampling frequency and locations of observation wells the analytical approach is not limited to groundwater applications but can be extended to any other mathematical problem with similar governing equations and under similar conceptual conditions this article is protected by copyright all rights reserved

connecting orbits for some classes of almost periodic lagrangian systems abstract the existence is proved by means of variational arguments of infinitely many heteroclinic solutions connecting possibly degenerate equilibria for a class of almost periodic lagrangian system an analogous multiplicity result is then established for homoclinic solutions of systems with an almost periodic singular potential

numerical solution of volterra fredholm integral equations via modification of hat functions abstract in this paper a new numerical approach is developed for solving linear and nonlinear volterra fredholm integral equations the fundamental structure of the presented method is based on the modification of hat functions the properties of modification of hat functions mhfs are first presented after implementation of our scheme the solution of the main problem would be transformed into the solution of a system of linear or nonlinear algebraic equations also an error analysis is provided under several mild conditions in addition examples are presented to illustrate the pertinent features of the method and the results are discussed

a geostatistical approach to the inverse problem in groundwater modeling steady state and one dimensional simulations the problem of estimating hydrogeologic parameters in particular permeability from input output measurements is reexamined in a geostatistical framework the field of the unknown parameters is represented as a random field and the estimation procedure consists of two main steps first the structure of the parameter field is identified i e mathematical representations of the variogram and the trend are selected and their parameters are established by using all available information including measurements of hydraulic head and permeability second linear estimation theory is applied to provide minimum variance and unbiased point estimates of hydrogeologic parameters kriging structure identification is achieved iteratively in three substeps structure selection maximum likelihood estimation and model validation and diagnostic checking the methodology was extensively tested through simulations on a simple one dimensional case the results are remarkably stable and well behaved the estimated field is smooth while small scale variability is statistically described as the quality of measurements improves the procedure reproduces more features of the original field the results are also shown to be rather insensitive to deviations from assumptions about the geostatistical structure of the field

existence and exponential decay of homoclinics in a nonperiodic superquadratic hamiltonian system abstract this paper deals with existence and exponential decay of homoclinic orbits in the first order hamiltonian system z j h z t z where the hamiltonian function h t z is nonperiodic in t r and superquadratic in z r 2 n with certain mild conditions we obtain the solutions via variational methods for strongly indefinite problems

positive solutions of asymptotically linear schrodinger poisson systems with a radial potential vanishing at infinity in this paper we study the schrodinger poisson system sp u v x u x u k x f u inr3 u2 u 0 inr3 and prove the existence of positive solutions for system sp when the nonlinearity f has growth at most linear for small allowing the potential v x to vanish at infinity in addition also we obtain the nonexistence of a nontrivial positive solution for 14

existence and multiplicity of semiclassical solutions for a schrodinger equation abstract we establish the existence and multiplicity of solutions for the semiclassical nonlinear schrodinger equation e 2 u v x u g x u for x r n u x 0 as x where e 0 is a small parameter and the potential v changes sign and may not be bounded from below and g x u is asymptotically linear in u as u

an iterative geostatistical inverse method for steady flow in the vadose zone an iterative geostatistical inverse approach is developed to estimate conditional effective unsaturated hydraulic conductivity parameters soil water pressure head and degree of saturation in heterogeneous vadose zones this approach is similar to the classical cokriging technique and it uses a linear estimator that depends on covariances and cross covariances of unsaturated hydraulic parameters soil water pressure head and degree of saturation the linear estimator is however improved successively by solving the governing flow equation and by updating the residual covariance and cross covariance functions in an iterative manner as a result the nonlinear relationship between unsaturated hydraulic conductivity parameters and head is incorporated in the estimation and the estimated fields are approximate conditional means the ability of the iterative approach is demonstrated through some numerical examples

numerical solution for three dimensional nonlinear mixed volterra fredholm integral equations via three dimensional block pulse functions we are concerned here with a three dimensional nonlinear mixed volterra fredholm integral equations of the second kind which include many key integral that appear in the theory of nonlinear parabolic boundary value problems the existence of a unique solution will be proved a new numerical method for solving these type of equations will be presented the method is based upon three dimensional block pulse functions approximation in addition convergence analysis of the method is discussed illustrative examples are included to demonstrate the validity and applicability of the technique

morse index and multiple solutions for the asymptotically linear schrodinger type equation abstract we study the nonlinear problem u v x u f x u x r n where the schrodinger type operator v is semibounded and has a finite number of eigenvalues below the infimum of the essential spectrum we classify the linear schrodinger equation prove the semi continuity and monotonicity of the index function and obtain some new conditions on the existence and multiplicity for generalized asymptotically linear schrodinger equations based on an application of the classical ambrosetti rabinowitz symmetric mountain pass theorem

multiplicity and concentration of homoclinic solutions for some second order hamiltonian systems abstract in this paper we present some new results of homoclinic solutions for second order hamiltonian systems u l t u w u t u 0 here 0 is a parameter l c r r n n and w c 1 r r n r unlike most other papers on this problem we require that l t is a positive semi definite symmetric matrix for all t r that is l t 0 is allowed to occur in some finite interval t of r under some suitable assumptions on w we prove the existence of two different homoclinic solutions u 1 u 2 which both vanish on r t as and converge to u 0 1 u 0 2 in h 1 r respectively here u 0 1 u 0 2 h 0 1 t are two nontrivial solutions of the dirichlet bvp for hamiltonian systems on the finite interval t

homoclinic orbits for a nonperiodic hamiltonian system abstract in this paper we prove the existence and multiplicity of homoclinic orbits for first order hamiltonian systems of the form z j h z t z where h z is asymptotically linear at and is not assumed to be periodic

an iterative stochastic inverse method conditional effective transmissivity and hydraulic head fields an iterative stochastic approach is developed to estimate transmissivity and head distributions in heterogeneous aquifers this approach is similar to the classical cokriging technique it uses a linear estimator that depends on the covariances of transmissivity and hydraulic head and their cross covariance the linear estimator is however improved successively by solving the governing flow equation and by updating the covariances and cross covariance function of transmissivity and hydraulic head fields in an iterative manner as a result the nonlinear relationship between transmissivity and head is incorporated in the estimation and the estimated fields are approximate conditional means the ability of the iterative approach is tested with some deterministic and stochastic inverse problems the results show that the estimated transmissivity and hydraulic head fields have smaller mean square errors than those obtained by classical cokriging even in the aquifer with variance of transmissivity up to 3

homoclinic orbits for asymptotically linear hamiltonian systems we study the existence of homoclinic orbits for first order time dependent hamiltonian systems z jhz z t where h z t depends periodically on t and hz z t is asymptotically linear in z as z we also consider an asymptotically linear schrodinger equation in rn

first order elliptic systems and the existence of homoclinic orbits in hamiltonian systems and h r x r 2 r is smooth by a homoclinic or a doubly asymptotic orbit to y where y is a periodic solution of 1 we mean a solution x y of 1 such that i x 0 y t l 0 as i tl oo finding homoclinic orbits in systems like 1 can be quite difficult in the case when y is a hyperbolic orbit this is equivalent to showing that the stable and unstable manifold of y intersect in some situation this can be done by melnikov s method recently some progress has been made by applying variational methods coti zelati and ekeland showed in 3 using dual variational methods that 1 has at least one homoclinic orbit if h satisfies some convexity and growth assumptions in their proof the convexity assumption enters in a crucial way already in the set up of the variational problem variational methods have been used by benci and giannoni 2 who studied homoclinic orbits on compact riemannian manifolds and by p rabinowitz in 9 who proved existence of heteroclinic orbits on the n dimensional torus as well as their multiplicity in 2 and 9 only special hamiltonian of lagrangian type are studied the associated variational problem is then at least semi definite the

solving system of linear stratonovich volterra integral equations via modification of hat functions this paper proposes an efficient method for solving system of linear stratonovich volterra integral equations stochastic operational matrix of modification of hat functions mhfs is determined by using mhfs and their stochastic operational matrix of integration a system of linear stratonovich volterra integral equations can be reduced to a linear system of algebraic equations thus we can solve the problem by direct methods also we prove that the rate of convergence is o h3 efficiency of this method and good degree of accuracy are confirmed by numerical examples

on the relation between the stratonovich and ogawa integrals l auteur montre que l existence de l integrale d ogawa implique l existence de l integrale de stratonovich et que les deux sont egales sous condition d une definition convenable de l integrale stochastique de stratonovich non adaptee

cokriging estimation of the conductivity field under variably saturated flow conditions a linear estimator cokriging was applied to estimate hydraulic conductivity using pressure head solute concentration and solute arrival time measurements in a hypothetical heterogeneous vadose zone under steady state infiltrations at different degrees of saturation covariances and cross covariances required by the estimator were determined by a first order approximation in which sensitivity matrices were calculated using an adjoint state method the effectiveness of the pressure concentration and arrival time measurements for the estimator were then evaluated using two statistical criteria l1 and l2 norms i e the average absolute error and the mean square error of the estimated conductivity field results of our analysis showed that pressure head measurements at steady state flow provided the best estimation of hydraulic conductivity among the three types of measurements in addition head measurements of flow near saturation were found more useful for estimating conductivity than those at low saturations the arrival time measurements do not have any significant advantage over concentration factors such as variability linearity and ergodicity were discussed to explain advantage and limitation of each type of data set finally to take advantage of different types of data set e g head and concentration a computationally efficient estimation approach was developed to combine them sequentially to estimate the hydraulic conductivity field the conductivity field estimated by using this sequential approach proves to be better than all the previous estimates using one type of data set alone

determining soil hydraulic properties by parameter estimation on the selection of a model for the hydraulic properties parameter estimation procedures involving solution of the inverse flow problem pertinent to a transient experiment constitute a powerful method of determining the soil hydraulic properties one of the problems associated with these procedures is the selection of an appropriate model to describe the soil hydraulic properties three different models were considered those of van genuchten vg and brooks and corey bc model and the exponential model of gardner for the hydraulic conductivity soil water pressure relationships coupled with a new expression for the soil water content soil water pressure relationship gr model for a given model the soil hydraulic properties were determined from simulated and measured outflow experiments supplemented with water content at a soil water pressure head of 15 000 cm h2o using the parameter estimation procedure of kool et al 1985a and data from two soils a hypothetical sandy loam soil assumed to be described by the vg model and a silt loam soil model validation tests were performed and the most appropriate model was selected from the candidate models by discrimination tests using the akaike information criterion aic in the case of the hypothetical sandy loam the vg model was found to be the most accurate and most consistent with the data the performance of both the bc and the gr models in terms of the aic was less good but very similar to each other in the case of the silt loam soil the vg model with additional parameter m which accounts for the correlation between pores and for the flow path tortuosity m 2 02 rather than a constant m 0 5 was found to be most accurate and most consistent with the data the performance of the bc and the gr models was similar when m was considered as an unknown parameter instead of a constant

existence and multiplicity results of homoclinic solutions for fractional hamiltonian systems abstract in this paper by the critical point theory we consider the existence and multiplicity of solutions for the following fractional differential equation t d d t u t l t u t w t u t t r where 1 2 1 d t and t d are left and right liouville weyl fractional derivatives of order on the whole axis r respectively u r n l t is positive definite symmetric matrix for all t r and w r r n r is a suitably chosen function

central limit theorem for a stratonovich integral with malliavin calculus this is the publisher s version also available electronically from http projecteuclid org euclid aop 1372859768

statistical analysis of spatial variability in unsaturated flow parameters core scale estimates of soil parameters of the gardner russo and van gemachten models of the hydraulic conductivity and water retention functions were obtained for 417 undisturbed soil cores taken from a wall of a trench 20 m long 2 5 m deep using a procedure based on inverse problem methodology these estimates were used to evaluate the first two statistical moments of the underlying random space functions rsfs using the restricted maximum likelihood estimation procedure coupled with the weighted least squares procedure to estimate parameters of models of the covariance and the drift functions of the pertinent rsfs the fitted models were used to evaluate the mean and covariance functions of the hydraulic conductivity and water rentention functions for given water saturations covariance functions of log saturated conductivity log ks and the shape parameters of the gardner russo and van genuchten models exhibited statistical anisotropy characterized by aspect ratios that vary between 3 to 4 correlation scales of log ks were larger than those of the shape parameters consequently the product of the variance of log unsaturated conductivity and its correlation scale remained essentially invariant for a considerable range of water saturation the implications of these results regarding stochastic modeling of transport in heterogeneous porous formations and possible applications of the results of this study are discussed briefly

existence and multiplicity of solutions for asymptotically linear nonperiodic hamiltonian elliptic system abstract this paper is concerned with the following nonperiodic hamiltonian elliptic system u v x u h v x u v v v x v h u x u v x r n u x v x 0 as x where z u v r n r r n 3 assuming the potential v is nonperiodic and sign changing h x z is nonperiodic in x and asymptotically quadratic in z u v existence and multiplicity of solutions are obtained via a variational approach

a reassessment of the groundwater inverse problem this paper presents a functional formulation of the groundwaterflow inverse problem that is sufficiently general to accommodate most commonly used inverse algorithms unknown hydrogeological properties are assumed to be spatial functions that can be represented in terms of a possibly infinite basis function expansion with random coefficients the unknown parameter function is related to the measurements used for estimation by a forward operator which describes the measurement process in the particular case considered here the parameter of interest is the large scale log hydraulic conductivity the measurements are point values of log conductivity and piezometric head and the forward operator is derived from an upscaled groundwaterflow equation the inverse algorithm seeks the most probable or maximum a posteriori estimate of the unknown parameter function when the measurement errors and parameter function are gaussian and independent the maximum a posteriori estimate may be obtained by minimizing a least squares performance index which can be partitioned into goodness of fit and prior terms when the parameter is a stationary random function the prior portion of the performance index is equivalent to a regularization term which imposes a smoothness constraint on the estimate this constraint tends to make the problem well posed by limiting the range of admissible solutions the gaussian maximum a posteriori problem may be solved with variational methods using functional generalizations of gauss newton or gradient based search techniques several popular groundwater inverse algorithms are either special cases of or variants on the functional maximum a posteriori algorithm these algorithms differ primarily with respect to the way they describe spatial variability and the type of search technique they use linear versus nonlinear the accuracy of estimates produced by both linear and nonlinear inverse algorithms may be measured in terms of a bayesian extension of the cramer rao lower bound on the estimation error covariance this bound suggests how parameter identifiability can be improved by modifying the problem structure and adding new measurements

some results on connecting orbits for a class of hamiltonian systems abstract the existence of various kinds of connecting orbits is established for a certain hamiltonian system as well as its time dependent analogue for the autonomous case our main assumption is that v has a global maximum e g at x o and we find a various kinds of orbits terminating at o for the time dependent case v has a local but not global maximum at x o and we find a homoclinic orbit emanating from and terminating at o keywords periodic solution

numerical treatment of stochastic differential equations we define general runge kutta approximations for the solution of stochastic differential equations sde these approximations are proved to converge in quadratic mean to the solution of an sde with a corrected drift the explicit form of the correction term is given concerning the order of convergence we show that in general it is impossible for the quadratic mean of the one step error to be of an order greater than o h 3 this order is attained e g by the stochastic analogue of heun s method in the n dimensional case the highest order of convergence is in general only o h 2 attained by euler s method the order o h 3 can only be reached if nabla x sigma r sigma s nabla x sigma s sigma r for the diffusion matrix

homoclinic orbits in a first order superquadratic hamiltonian system convergence of subharmonic orbits abstract we consider the existence of homoclinic orbits for a first order hamiltonian system z jh z t z we assume h t z is of form h t z 1 2 az z w t z where a is a symmetric matrix with ja i r and w t z is 2 periodic in t and has superquadratic growth in z we prove the existence of a nontrivial homoclinic solution z t and subharmonic solutions zt t t n i e 2 t periodic solutions of hs such that zt t z t in cloc1 r r 2n as t

on a periodic schrodinger equation with nonlocal superlinear part we consider the choquard pekar equation open image in new window and focus on the case of periodic potential v for a large class of even functions w we show existence and multiplicity of solutions essentially the conditions are that 0 is not in the spectrum of the linear part v and that w does not change sign our results carry over to more general nonlinear terms in arbitrary space dimension n 2

homoclinic orbits for a singular second order neutral differential equation using critical point theory and an approximation method we study the existence of homoclinic orbits for a singular second order neutral differential difference equations

existence and multiplicity of homoclinic orbits for the second order hamiltonian systems in this paper we study the following nonperiodic second order hamiltonian system u t l t u t ur t u t r where l t may not be uniformly positive definite for all t r and r t u is asymptotically quadratic in u as u by applying a generalized linking theorem in bartsch and ding 2006 8 we obtain the existence and multiplicity of homoclinic orbits for the above system

existence and multiplicity of semiclassical solutions for asymptotically hamiltonian elliptic systems abstract this paper is concerned with the following nonperiodic hamiltonian elliptic system e 2 u v x u h u x u v in r n e 2 v v x v h v x u v in r n u x 0 and v x 0 as x where e 0 is a small parameter and the potential v is bounded below and h is asymptotically linear in z as z with z u v by applying a generalized linking theorem of strongly indefinite functionals we obtain the existence of multiple semiclassical solutions for the above system

existence and multiplicity of solutions for a non periodic schrodinger equation abstract this paper is concerned with the non periodic schrodinger equation u v x u f x u x r n u x 0 as x under a general spectral assumption the existence and multiplicity of solutions are obtained for asymptotically linear nonlinearity via variational methods

nonstationary homoclinic orbits for an infinite dimensional hamiltonian system we study the following system of diffusion equations on r rn tu xu v x u g t x v tv xv v x v f t x u where z u v r rn r2 v c rn r g t x v f t x u are periodic in t x and superlinear at infinity by a variant linking theorem and concentration compactness arguments we establish the existence of nonstationary homoclinic type solutions of least energy for this systems

stability of the multi jensen equation abstract in this paper we study the stability in the sense of th m rassias of multi jensen equation

multiple solutions for asymptotically quadratic and superquadratic elliptic system of hamiltonian type this paper is concerned with the following nonperiodic hamiltonian elliptic system u v x u h v x u v x r n v v x v h u x u v x r n u x 0 v x 0 as x where z u v r n r i r n 3 and the potential v x is nonperiodic and sign changing by applying a generalized linking theorem for strongly indefinite functionals we establish the existence of multiple solutions for asymptotically quadratic nonlinearity as well as the existence of infinitely many solutions for superquadratic nonlinearity

homoclinic orbits on compact manifolds abstract under a suitable assumption on the potential energy v we prove the existence of a homoclinic orbit of the equation dt x t grad v x t 0 x m where m is a compact riemannian manifold our assumption is satisfied for instance if the function v has a unique nondegenerate maximum point

approximation solution of nonlinear stratonovich volterra integral equations by applying modification of hat functions in this paper we studied the hyers ulam rassias stability for nonlinear stratonovich volterra integral equations also we obtained stochastic operational matrix of modification of hat functions mhfs to numerically solve the nonlinear stratonovich volterra integral equations the main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved finally numerical examples are presented to certify convergence and accuracy of the method

on the complexity of stochastic integration we study the complexity of approximating stochastic integrals with error e for various classes of functions for ito integration we show that the complexity is of order e 1 even for classes of very smooth functions the lower bound is obtained by showing that ito integration is not easier than lebesgue integration in the average case setting with the wiener measure the upper bound is obtained by the milstein algorithm which is almost optimal in the considered classes of functions the milstein algorithm uses the values of the brownian motion and the integrand it is bilinear in these values and is very easy to implement for stratonovich integration we show that the complexity depends on the smoothness of the integrand and may be much smaller than the complexity of ito integration

application of operational matrices for solving system of linear stratonovich volterra integral equation abstract in this paper we give a brief review on block pulse functions bpfs and obtain operational matrix and stochastic operational matrix of integration based on bpfs then these operational matrices are used to solve system of linear stratonovich volterra integral equations by applying proposed method the system of linear stratonovich volterra integral equations reduce to system of linear algebraic equations which can be solved by a convenient numerical method also the error analysis is proved under several mild conditions we show the rate of convergence is o h finally by applying this method on two examples we demonstrate accuracy and efficiency of the proposed method all of the numerical calculation are performed on computer using a program written in matlab

homoclinic solutions for some second order non autonomous hamiltonian systems without the globally superquadratic condition abstract this paper deals with the existence of homoclinic solutions for the following second order non autonomous hamiltonian system hs q v q t q f t where v c 1 r r n r v t q k t q w t q is t periodic in t f is aperiodic and belongs to l 2 r r n under the assumptions that k satisfies the pinching condition b 1 q 2 k t q b 2 q 2 w t q is not globally superquadratic on q and some additionally reasonable assumptions we give a new existence result to guarantee that hs has a homoclinic solution q t emanating from 0 the homoclinic solution q t is obtained as a limit of 2 k t periodic solutions of a sequence of the second order differential equations and these periodic solutions are obtained by the use of a standard version of the mountain pass theorem recent results in the literature are generalized and significantly improved

infinitely many stationary solutions of discrete vector nonlinear schrodinger equation with symmetry in this paper we study the existence of stationary solutions for the following discrete vector nonlinear schrodinger email protected email protected email protected email protected f email protected email protected n jf n f n f n where f n is a sequence of 2 component vector j 0110 email protected email protected n email protected n email protected nis the discrete laplacian in one spatial dimension and sequence t n is assumed to be n periodic in n i e t n email protected n we prove the existence of infinitely many nontrivial stationary solutions for this system by variational methods the same method can also be applied to obtain infinitely many breather solutions for single discrete nonlinear schrodinger equation