fully nonlinear fourth order equations with functional boundary conditions abstract the aim of this paper consists in to give sufficient conditions to ensure the existence and location of the solutions of a nonlinear fully fourth order equation with functional boundary conditions the arguments make use of the upper and lower solutions method a laplacian operator and a fixed point theorem an application of the beam theory to a nonlinear continuous model of the human spine allows to estimate its deformation under some loading forces

extremal solutions of φ laplacian diffusion scalar problems with nonlinear functional boundary conditions in a unified way abstract the aim of this paper is to ensure the existence of extremal solutions lying between a pair of lower and upper solutions for a second order differential equation that includes both the laplacian and some classes diffusion equations the results hold from a suitable change of variables an example is given to expose the applicability of the obtained results

on the solvability of some discontinuous third order nonlinear differential equations with two point boundary conditions abstract we prove the existence of extremal solutions for the third order discontinuous functional nonlinear problem u t f t u u t u t for a e t a b u a a a r l 1 u u u a u b u a 0 l 2 u u a u b u b 0 by using a fixed point theorem after having established some existence results for some auxiliary second order nonlinear problems we observe that together with the discontinuities allowed on the spacial variable u with adequate modifications of technical type analogous results can be obtained when the equation has a second member not necessarily continuous in u

solvability of strongly nonlinear boundary value problems for second order differential inclusions abstract in this paper we study a problem for a second order differential inclusion with dirichlet neumann and mixed boundary conditions the equation is driven by a nonlinear not necessarily homogeneous differential operator satisfying certain conditions and containing as a particular case the p laplacian operator we prove the existence of solutions both for the case in which the multivalued nonlinearity has convex values and for the case in which it has not convex values the presence of a maximal monotone operator in the equation make the results applicable to gradient systems with non smooth time invariant convex potential and differential variational inequalities

dynamics of excitation in systems with a randomly modulated decay channel abstract we have investigated the kinetics of excitation in the frame of the conventional pauli master equation for a molecular aggregate with a decay channel attached to one distinguished molecule or site as a principally new feature we assume the rate of probability flow through the decay channel to be a randomly modulated function of time the modulation is described by a markoff stochastic process and we do not invoke the white noise assumption an exact calculation is given for a broad family of stochastic processes which bridges and includes the asymmetric random telegraph signal and the gaussian process the general method is then applied in three physically relevant situations one molecule aggregate cyclic antenna system and infinite linear chain in these models we discuss the site occupation probabilities the aggregate excitation function and the mean de excitation time

from two state jump to gaussian stochastic processes abstract a stochastic process which bridges the two state jump markoff process and the gaussian process is introduced and fundamental properties of the process are fully analyzed the resulting expressions are combined with the partial cumulant expansion formula to give an exact power spectrum in the form of a continued fraction a rigorous expression is also obtained for a relaxation function in an analytic form

implicit nonlinear discontinuous functional boundary value φ laplacian problems extremality results this paper is devoted to the study of the following implicit nonlinear discontinuous functional boundary value problem ip l 0u t f t u l 0u fora e t i a b l 1 u b 1 u l 1 u 0 l 2 u a u b wherel 0u t ddt f t u t u t g t u u t u t andl 1 u l 1 u a u b u a u b u supposing that there is a lower solution a and an upper solution b such that a b the existence of extremal solutions lying between both functions is proved

one dimensional φ laplacian functional equations abstract in this paper we study functional laplacian equations with functional boundary conditions the non linearity belongs to a class of completely continuous operators which includes caratheodory ones while the functional boundary conditions are given by compactly fixed operators we extend in particular a solvability result of c bereanu and j mawhin

a solvable model of dielectric relaxation abstract dielectric relaxation phenomena are analyzed with an exactly solvable model this is such a general model that it includes typical stochastic processes and models as special cases the solutions in the frequency domain as well as in the time domain are obtained and dielectric function e is explicitly calculated

fourth order problems with nonlinear boundary conditions we develop a new method of lower and upper solutions for a fourth order nonlinear boundary value problem where the differential equation has dependence on all lower order derivatives our boundary conditions are nonlinear we will assume the functions that define the nonlinear boundary conditions are either monotone or nonmonotone as a result we obtain existence principles which improve recent results in the literature

a new class of models for bivariate joint tails summary a fundamental issue in applied multivariate extreme value analysis is modelling dependence within joint tail regions the primary focus of this work is to extend the classical pseudopolar treatment of multivariate extremes to develop an asymptotically motivated representation of extremal dependence that also encompasses asymptotic independence starting with the usual mild bivariate regular variation assumptions that underpin the coefficient of tail dependence as a measure of extremal dependence our main result is a characterization of the limiting structure of the joint survivor function in terms of an essentially arbitrary non negative measure that must satisfy some mild constraints we then construct parametric models from this new class and study in detail one example that accommodates asymptotic dependence asymptotic independence and asymmetry within a straightforward parsimonious parameterization we provide a fast simulation algorithm for this example and detail likelihood based inference including tests for asymptotic dependence and symmetry which are useful for submodel selection we illustrate this model by application to both simulated and real data in contrast with the classical multivariate extreme value approach which concentrates on the limiting distribution of normalized componentwise maxima our framework focuses directly on the structure of the limiting joint survivor function and provides significant extensions of both the theoretical and the practical tools that are available for joint tail modelling

on discontinuous first order implicit boundary value problems t 0 1 2 under various boundary conditions cf e g 1 5 8 13 29 31 32 thereis little known about the existence of solutions of 1 2 even in the casewhen f is continuous unless it is possible to solve the equation 1 2 forthe highest derivative and then to apply standard existence theory such asleray schauder theory one approach taken for instance in 8 16 is toreduce equation 1 2 to a differential inclusion of the formu

higher order boundary value problems with φ laplacian and functional boundary conditions we study the existence of solutions of the boundary value problem f u n 1 t f t u t u t u n 1 t 0 email protected 0 1 g i u u u n 1 u i 0 0 i 0 n 2 g n 1 u u u n 1 u n 2 1 0 where n 2 f and g i i 0 n 1 are continuous and f is a caratheodory function we obtain an existence criterion based on the existence of a pair of coupled lower and upper solutions we also apply our existence theorem to derive some explicit conditions for the existence of a solution of a special case of the above problem in our problem both the differential equation and the boundary conditions may have dependence on all lower order derivatives of the unknown function and many boundary value problems with various boundary conditions studied extensively in the literature are special cases of our problem consequently our results improve and cover a number of known results in the literature examples are given to illustrate the applicability of our theorems

on singular functional nonsmooth and implicit phi laplacian initial and boundary value problems in this paper we apply fixed point results for mappings in partially ordered spaces to derive existence results for extremal solutions of phi laplacian initial and boundary value problems the considered problems can be singular functional discontinuous nonlocal and implicit concrete examples are also solved

on the one dimensional p laplacian with a singular nonlinearity abstract in this paper we are concerned with the existence and nonexistence of positive solutions of boundary value problems for the one dimensional p laplacian with a singular nonlinearity in the case of the model equation we give the necessary and sufficient conditions of the existence of positive solutions for both the dirichlet problem and the periodic problem

weighted approximations of tail copula processes with application to testing the bivariate extreme value condition consider n i i d random vectors on r 2 with unknown common distribution function f under a sharpening of the extreme value condition on f we derive a weighted ap proximation of the corresponding tail copula process then we construct a test to check whether the extreme value condition holds by comparing two estimators of the limiting extreme value dis tribution one obtained from the tail copula process and the other obtained by first estimating the spectral measure which is then used as a building block for the limiting extreme value distribu tion we derive the limiting distribution of the test statistic from the aforementioned weighted approximation this limiting distribution contains unknown functional parameters therefore we show that a version with estimated parameters converges weakly to the true limiting distribution based on this result the finite sample properties of our testing procedure are investigated through a simulation study a real data application is also presented

existence theory for functional p laplacian equations with variable exponents in this paper we consider the solvability of equations of the form d dt t u u t u t f t u u t u t for a e t i a b subject to a general type of functional boundary conditions which cover dirichlet and periodic boundary data as particular cases our approach is that of upper and lower solutions together with growth restrictions of nagumo s type an example is provided where a p laplacian with variable p is shown to have a solution between given upper and lower solutions

extremal solutions for nonlinear functional ϕ laplacian impulsive equations abstract in this paper we deal with some nonlinear laplacian second order boundary value problems with impulses subject to a general type of boundary value conditions which cover dirichlet and periodic boundary data as particular cases our approach is that of upper and lower solutions together with growth restrictions of nagumo s type the impulsive functions depend implicitly on the different considered variables and the boundary value conditions are nonlinear in both cases functional dependence on the solution is allowed

nonparametric estimation of the spectral measure of an extreme value distribution let x 1 y 1 x n y n be a random sample from a bivariate distribution function f in the domain of max attraction of a distribution function g this g is characterised by the two extreme value indices and its spectral or angular measure the extreme value indices determine both the marginals and the spectral measure determines the dependence structure of g one of the main issues in multivariate extreme value theory is the estimation of this spectral measure we construct a truly nonparametric estimator of the spectral measure based on the ranks of the above data under natural conditions we prove consistency and asymptotic normality for the estimator in particular the result is valid for all values of the extreme value indices the theory of local empirical processes is indispensable here the results are illustrated by an application to real data and a small simulation study

existence result for a third order ode with nonlinear boundary conditions in presence of a sign type nagumo control abstract in this work we provide an existence and location result for the third order nonlinear differential equation u t f t u t u t u t where f a b r 3 r is a continuous function and two types of boundary conditions u a a u b u b 0 u a b or u a a u a u a 0 u b c with r 2 r continuous functions monotonous in the second variable and a b c r we assume that f satisfies a sign type nagumo condition which allows an asymmetric unbounded behaviour on the nonlinearity the arguments used concern leray schauder degree theory and lower and upper solutions technique

positive solutions for one dimensional p laplacian boundary value problems with sign changing nonlinearity abstract this paper deals with the existence of positive solutions for the one dimensional p laplacian p u f t u u 0 t 0 1 subject to the boundary value conditions u 0 i 1 n i u i u 1 i 1 n i u i where p s s p 2 s p 1 we show that it has at least one or two positive solutions under some assumptions by applying the fixed point theorem the interesting points are that the nonlinear term f is involved with the first order derivative explicitly and f may change sign

multiple positive solutions to a class of singular boundary value problems for the one dimensional p laplacian abstract in this paper we establish the existence of multiple positive solutions to the singular nonlinear boundary value problem u q t f u t 0 0 1 the singularity may appear at u 0 and t 0

stochastic theory of a quasiparticle propagating in a dynamically fluctuating medium abstract a stochastic theory describing properties of a quasiparticle propagating in a dynamically fluctuating medium is developed on the basis of the single site dynamical coherent potential approximation and the time convolution equation formalism involving the partial cumulant expansion the optical absorption spectra i the density of states n and the diffusion constant d are calculated for the quasiparticle suffering site energy diagonal fluctuations consisting of an arbitrary number of two state jump markoff processes with an asymmetric probability distribution of the stochastic variable with these fluctuations we have interpolated a two state jump markoff process and a gaussian markoff process and described the behavior of i n and d related to the intermediate processes effects of the asymmetric distribution which may be ascribed to the temperature of the fluctuating medium on i n and d have also been clarified including a tendency for d to increase with increasing asymmetry

numerical analysis of diffusion of a quasiparticle in a dynamically fluctuating medium based on the path integral method ii abstract the path integral method is applied to the study of a stochastic hamiltonian describing the motion of a quasiparticle in a dynamically fluctuating medium formulas to calculate the density of states and the diffusion constant of the quasiparticle are derived on the basis of the path integral method which enables us to compute their exact values numerically for arbitrary fluctuations numerical calculation is demonstrated for one dimensional systems with site energy fluctuations obeying an asymmetric two state jump markoff process as far as one particle quantities such as the density of states are concerned no marked discrepancy between our results and those of the coherent potential approximation are observed as for the diffusion constant on the other hand the two results exhibit qualitatively different behavior which is related to the localization of a quasiparticle particularly for slow fluctuations

a necessary and sufficient condition for existence of positive solutions of nonlinear boundary value problems abstract we study the nonlinear boundary value problem u f t u u u t 0 1 u 2 i 0 u 2 i 1 0 i 0 1 and obtain a necessary and sufficient condition for the existence of symmetric positive solutions we also discuss the application of our result to the special case where f is a power function of u and its derivatives moreover similar conclusions for a more general higher order boundary value problem are established our analysis mainly relies on the lower and upper solution method

the monotone method for neumann functional differential equations with upper and lower solutions in the reverse order abstract in this paper we show that the monotone technique produces two monotone sequences that converge uniformly to extremal solutions of second order functional differential equations and laplacian equations with neumann boundary value conditions moreover we obtain existence results assuming upper and lower solutions in the reverse order

maximum empirical likelihood estimation of the spectral measure of an extreme value distribution consider a random sample from a bivariate distribution function f in the max domain of attraction of all extreme value distribution function g this g is characterized by two extreme value indices and a spectral measure the latter determining the tail dependence structure of f a major issue in multivariate extreme value theory is the estimation of the spectral measure 1 p with respect to the l p norm for every p is an element of 1 infinity a nonparametric maximum empirical likelihood estimator is proposed for phi p the main novelty is that these estimators are guaranteed to satisfy the moment constraints by which spectral measures are characterized asymptotic normality of the estimators is proved under conditions that allow for tail independence moreover the conditions are easily verifiable as we demonstrate through a number of theoretical examples a simulation study shows a substantially improved performance of the new estimators two case studies illustrate how to implement the methods in practice

non parametric bayesian inference on bivariate extremes the tail of a bivariate distribution function in the domain of attraction of a bivariate extreme value distribution may be approximated by the one of its extreme value attractor the extreme value attractor has margins that belong to a three parameter family and a dependence structure which is characterised by a probability measure on the unit interval with mean equal to one half called spectral measure inference is done in a bayesian framework using a censored likelihood approach a prior distribution is constructed on an in nite dimensional model for this measure the model being at the same time dense and computationally manageable a trans dimensional markov chain monte carlo algorithm is developed and convergence to the posterior distribution is established in simulations the bayes estimator for the spectral measure is shown to compare favorably with frequentist nonparametric estimators an application to a data set of danish re insurance claims is provided

solvability of some third order boundary value problems with asymmetric unbounded nonlinearities abstract in this paper we present existence and location results for the third order separated boundary value problems u t f t u t u t u t with the boundary conditions u a a u a b u b c or u a a c 1 u a c 2 u a b c 3 u b c 4 u b c with c 1 c 2 c 3 c 4 r and a b c r we assume f a b r 3 r is a continuous function satisfying one sided nagumo type condition which allows an asymmetric unbounded behaviour the arguments used concern leray schauder degree and lower and upper solution techniques

upper and lower solutions for second order boundary value problems with nonlinear boundary conditions on demontre des theoremes d existence en utilisant des solutions superieures et inferieures