on lp x norms the relation between a banach function space x and its subspaces formed by i those functions with absolutely continuous norm ii those with continuous norm and iii the closure of the set of

the existence of multiple equilibrium points in a global attractor for some p laplacian equation abstract in this paper we are mainly concerned with some properties of the global attractor for some p laplacian equation with a lyapunov function in a banach space under some suitable assumptions we prove the existence of multiple equilibrium points in a global attractor for some p laplacian equation

a hybrid asymptotic numerical method for low reynolds number flows past a cylindrical body the classical problem of slow steady two dimensional flow of a viscous incompressible fluid around an infinitely long straight cylinder is considered the cylinder cross section is symmetric about the direction of the oncoming stream but otherwise is arbitrary for low reynolds number the well known singular perturbation analysis for this problem shows that the asymptotic expansions of the drag coefficient and of the flow field start with infinite logarithmic series we show that the entire infinite logarithmic expansions of the flow field and of the drag coefficient are contained in the solution to a certain related problem that does not involve the cross sectional shape of the cylinder the solution to this related problem is computed numerically using a straightforward finite difference scheme the drag coefficient for a cylinder of a specific cross sectional shape which is asymptotically correct to within all logarithmic terms is given in terms of a single shape dependent constant that is determi

varying boundary conditions in a general class of elliptic problems of mixed type abstract in this paper we use the linear theory developed in cano casanova and lopez gomez j differential equations 178 2002 123 to show the continuous dependence of the positive solutions of a general class of sublinear elliptic boundary value problems of mixed type with respect to the boundary operator besides working with mixed non classical boundary conditions this paper considers problems where bifurcation from infinity occurs treating this kind of problems is far from easy since a complete knowledge of the set of values of the parameters where they exhibit a positive solution is imperative our results are far from immediate as a consequence of the vanishing weight functions involved in our general setting now a days the analysis of these general problems where the coefficients are allowed to vary and eventually vanishing or changing sign is focusing a great deal of attention

multiple solutions for an eigenvalue problem involving p laplacian type operators abstract in this paper we establish the existence of two nontrivial weak solutions of some eigenvalue problems involving a general elliptic operator in divergence form first we study a one parameter problem under homogeneous dirichlet boundary conditions in bounded domains and then a two parameters problem under inhomogeneous nonlinear robin boundary conditions in regular bounded domains these results complete in several directions some recent papers where a ricceri type critical point theorem was used the main argument of this paper is based on two recent theorems due to arcoya and carmona 2007 in 2 which we use in a slightly modified version see section 2

some qualitative questions on the equation div a x u u f x u abstract in this article we establish several applications of picone s identity for the operator of the form d i v a x u u such as hardy type inequality sturmian comparison theorem monotonicity property of the first eigenvalue nonexistence of positive supersolutions and caccioppoli inequality under certain conditions on a

uniform asymptotic approximation of diffusion to a small target generalized reaction models the diffusion of a reactant to a binding target plays a key role in many biological processes the reaction radius at which the reactant and target may interact is often a small parameter relative to the diameter of the domain in which the reactant diffuses we develop uniform in time asymptotic expansions in the reaction radius of the full solution to the corresponding diffusion equations for two separate reactant target interaction mechanisms the doi or volume reactivity model and the smoluchowski collins kimball partial absorption surface reactivity model in the former the reactant and target react with a fixed probability per unit time when within a specified separation in the latter upon reaching a fixed separation they probabilistically react or the reactant reflects away from the target expansions of the solution to each model are constructed by projecting out the contribution of the first eigenvalue and eigenfunction to the solution of the diffusion equation and then developing matched asymptotic expansions in laplace transform space our approach offers an equivalent but alternative method to the pseudopotential approach we previously employed isaacson and newby phys rev e 88 012820 2013 pleee81539 375510 1103 physreve 88 012820 for the simpler smoluchowski pure absorption reaction mechanism we find that the resulting asymptotic expansions of the diffusion equation solutions are identical with the exception of one parameter the diffusion limited reaction rates of the doi and partial absorption models this demonstrates that for biological systems in which the reaction radius is a small parameter properly calibrated doi and partial absorption models may be functionally equivalent

combined instrumental variable and subspace fitting approach to parameter estimation of noisy input output systems the paper considers the problem of estimating the parameters of linear discrete time systems from noise corrupted input output measurements under fairly general conditions the output and input noises may be auto correlated and they may be cross correlated as well by using the instrumental variable iv principle a covariance matrix is obtained the singular vectors of which bear complete information on the parameters of the system under study a weighted subspace fitting wsf procedure is then employed on the sample singular vectors to derive estimates of the parameters of the system the combined iv wsf method proposed in the present paper is noniterative and simple to use its large sample statistical performance is analyzed in detail and the theoretical results so obtained are used to predict the behavior of the method in samples with practical lengths several numerical examples are included to show the agreement between the theoretically predicted and the empirically observed performances

nonuniformly elliptic equations of p laplacian type abstract this paper deals with the existence of a generalized solution in w 0 1 p to a nonuniformly nonlinear elliptic equation of the form div a x u f x u in a bounded domain of r n here a satisfies a x c 0 h 0 x h 1 x p 1 for any in r n a e x h 0 l p p 1 and h 1 l loc 1

brief paper on the identifiability of errors in variables models with white measurement errors we discuss identifiability of dynamic siso errors in variables eiv models with white measurement errors although this class of models turns out to be generically identifiable it has been pointed out that in certain circumstances there may be two eiv models which are indistinguishable from external input output experiments this lack of global identifiability may be prejudicial to identification and needs better understanding the identifiability conditions found in the literature guarantee uniqueness under certain coprimality assumptions on the rational transfer function of the ideal true system and the spectral density of the noiseless true input unfortunately these conditions are not testable since they concern precisely the unknowns of the problem which are not available to the experimenter we provide new identifiability conditions which are instead expressible in terms of the external description of the observable signals namely their joint power spectral densities

perturbation of eigenvalues due to gaps in two dimensional boundaries motivated by problems involving diffusion through small gaps we revisit two dimensional eigenvalue problems with localized perturbations to neumann boundary conditions we recover the known result that the gravest eigenvalue is o ln 1 where is the ratio of the size of the hole to the length scale of the domain and provide a simple and constructive approach for summing the inverse logarithm terms and obtaining further corrections comparisons with numerical solutions obtained for special geometries both for the dirichlet patch problem where the perturbation to the boundary consists of a different boundary condition and for the gap problem confirm that this approach is a simple way of obtaining an accurate value for the gravest eigenvalue and hence the long term outcome of the underlying diffusion problem

the mean first rotation time of a planar polymer we estimate the mean first time called the mean rotation time mrt for a planar random polymer to wind around a point this polymer is modeled as a collection of n rods each of them being parameterized by a brownian angle we are led to study the sum of i i d imaginary exponentials with one dimensional brownian motions as arguments we find that the free end of the polymer satisfies a novel stochastic equation with a nonlinear time function finally we obtain an asymptotic formula for the mrt whose leading order term depends on the square root of n and interestingly depends weakly on the mean initial configuration our analytical results are confirmed by brownian simulations our analytical results are confirmed by brownian simulations

strongly consistent coefficient estimate for errors in variables models for the single input single output siso errors in variables system it is assumed that the system input is an arma process and that the driven noise of the system input and the observation noise are jointly gaussian the two dimensional observation made on system input and output is represented as a two dimensional 2d arma system of minimum phase driven by a sequence of 2d i i d gaussian random vectors innovation representation it is shown that the resulting arma system is identifiable i e its coefficients are uniquely defined under reasonable conditions recursive algorithms are proposed for estimating coefficients of the arma representation including those contained in the original siso system the estimates are proved to be convergent to the true values with probability one and the convergence rate is derived as well the theoretical results are justified by numerical simulation

a three critical points theorem revisited abstract in this paper the following result is proved let x be a reflexive real banach space i r an interval x r a sequentially weakly lower semicontinuous c 1 functional bounded on each bounded subset of x whose derivative admits a continuous inverse on x j x r a c 1 functional with compact derivative assume that lim x x j x for all i and that there exists r such that sup i inf x x x j x inf x x sup i x j x then there exist a non empty open set a i and a positive real number r with the following property for every a and every c 1 functional x r with compact derivative there exists 0 such that for each 0 the equation x j x x 0 has at least three solutions in x whose norms are less than r

domain perturbation for elliptic equations subject to robin boundary conditions abstract we prove domain perturbation theorems for linear and nonlinear elliptic equations under robin boundary conditions the theory allows very singular perturbation of domains in particular it includes cutting holes parts degenerating to a set of measure zero such as the dumbbell problem or wildly oscillating boundaries in the last case we show that the limiting problem is the dirichlet problem

narrow escape problem with a mixed trap and the effect of orientation we consider the mean first passage time mfpt of a two dimensional diffusing particle to a small trap with a distribution of absorbing and reflecting sections high order asymptotic formulas for the mfpt and the fundamental eigenvalue of the laplacian are derived which extend previously obtained results and show how the orientation of the trap affects the mean time to capture we obtain a simple geometric condition which gives the optimal trap alignment in terms of the gradient of the regular part of a regular part of a green s function and a certain alignment vector we find that subdividing the absorbing portions of the trap reduces the mean first passage time of the diffusing particle in the scenario where the trap undergoes prescribed motion in the domain the mfpt is seen to be particularly sensitive to the orientation of the trap

strong localized perturbations of eigenvalue problems this paper considers the effect of three types of perturbations of large magnitude but small extent on a class of linear eigenvalue problems for elliptic partial differential equations in bounded o

identification of errors in variables systems with arma observation noises abstract the purpose of the paper is to give the recursive estimate for coefficients of the single input single output siso errors in variables eiv system and to prove its strong consistency the observation noises of the eiv system are assumed to be arma processes and the system input is taken to be an iid sequence the recursive estimation algorithm is given with the help of stochastic approximation sa method and the strong consistency is established under reasonable conditions the numerical simulation is consistent with the theoretical analysis

time delay estimation in unknown gaussian spatially correlated noise a novel class of methods that estimate the difference in arrival time between signals corrupted by spatially correlated gaussian noise sources of unknown cross correlation is presented the methods are based on the idea of comparing the similarities between the two sensor measurements in higher order spectrum domains bispectrum rather than in the cross correlation domain it is demonstrated that estimation techniques based on higher order cumulants suppress the effect of correlated gaussian noise sources and therefore exhibit improved performance over generalized cross correlation methods results are reported for different types of signals lengths of data records and signal to noise ratios

adaptive rejection of non linear disturbances in extended non linear output feedback systems this paper deals with asymptotic rejection of disturbances generated from non linear exosystems for uncertain nonlinear systems in an extended output feedback form which allows the vector field coupled with the system input to have different nonlinear functions of the system output as its elements a new internal model design is proposed to deal with nonlinear functions of the system output that are coupled with the input and the unknown disturbance adaptive control techniques are then used to deal with the uncertainty in the system the proposed adaptive disturbance rejection algorithm with the new internal model design ensures the asymptotic rejection of the unknown nonlinear disturbance and the boundedness of all the variables

a fourth order accurate method for the incompressible navier stokes equations on overlapping grids a method is described to solve the time dependent incompressible navier stokes equations with finite differences on curvilinear overlapping grids in two or three space dimensions the scheme is fourth order accurate in space and uses the momentum equations for the velocity coupled to a poisson equation for the pressure the boundary condition for the pressure is taken as u 0 extra numerical boundary conditions are chosen to make the scheme accurate and stable the velocity is advanced explicitly in time any standard time stepping scheme such as runge kutta can be used the poisson equation is solved using direct or iterative sparse matrix solvers or by the multigrid algorithm computational results in two and three space dimensions are given

multiple solutions for p harmonic type equations abstract in this paper we establish the existence of multiple solutions for an equation involving a p harmonic operator subject to dirichlet boundary conditions in a bounded smooth open domain of r n while the nonlinearity has a p 1 sublinear growth at infinity using a three critical points theorem we prove the existence of at least three distinct weak solutions in w 0 2 p to this problem

summing logarithmic expansions for singularly perturbed eigenvalue problems strong localized perturbations of linear and nonlinear eigenvalue problems in a bounded two dimensional domain d are considered the effects on an eigenvalue lambda 0 of the lapla cian and on the fold point lambda c0 of a nonlinear eigenvalue problem of removing a small subdomain d epsilon of radius epsilon from d and imposing a condition on the boundary of the resulting hole are determined using the method of matched asymptotic expansions it is shown that the expansions of the eigenvalues and fold points for these perturbed problems start with infinite series in powers of 1 log epsilon d kappa here d kappa is a constant that depends on the shape of d epsilon and on the precise form of the boundary condition on the hole in each case it is shown that the entire infinite series is contained in the solution of a single related problem that does not involve the size or shape of the hole this related problem is not stiff and can be solved numerically

some remarks on a three critical points theorem abstract some remarks on a strict minimax inequality which plays a fundamental role in ricceri s three critical points theorem are presented as a consequence some recent applications of ricceri s theorem to nonlinear boundary value problems are revisited by obtaining more precise conclusions

identification of errors in variables systems with nonlinear output observations this paper concerns the identification problem of errors in variables eiv systems with nonlinear output observations under independent and identically distributed iid gaussian inputs with unknown variance recursive algorithms for estimating the parameters of the eiv systems are presented for a large class of nonlinear observations conditions on the system are imposed to guarantee the almost sure convergence of the estimates some simulation examples are included to justify the theoretical results

diffusion escape through a cluster of small absorbing windows we study the first eigenvalue of the laplace equation in a bounded domain in r d d 2 3 with mixed neumann dirichlet zaremba boundary conditions the neumann condition is imposed on most of the boundary and the dirichlet boundary consists of a cluster of small windows when the windows are well separated the first eigenvalue is asymptotically the sum of eigenvalues of mixed problems with a single dirichlet window however when two or more dirichlet windows cluster tightly together they interact nonlinearly we compare our asymptotic approximation of the eigenvalue to the escape rate of simulated brownian particles through the small windows

ground states of degenerate quasilinear schrodinger equation with vanishing potentials abstract in this paper we study the existence of nontrivial ground state solutions for the following class of p laplacian type equation div a x u v x x p u p 2 u k x x p f u in r n where 1 p n n 3 n p p e 1 d 1 e p p e n p n d p critical hardy sobolev exponent f has a quasicritical growth v and k are nonnegative potentials the function a satisfies a x u c 0 x p h 0 x u p 1 c 0 1 x p h 1 x u p 1 for any r n a e x r n for any two positive functions h 1 l l o c r n h 0 l p p 1 r n with p p

on the uniqueness of prediction error models for systems with noisy input output data abstract this paper addresses the uniqueness problem of the prediction error pe identification for a class of linear systems with noisy input and output data necessary and sufficient conditions are derived for the corresponding pe loss function to have asymptotically a unique global minimum the results indicate that a pe algorithm may give very bad parameter estimates for systems not satisfying these conditions such a possibility is illustrated by a numerical example while the pe method is used as a vehicle for illustration the derived conditions for global uniqueness or identifiability apply to any consistent estimation method based on second order data

stability of solitary waves in finite ablowitz ladik lattices we discuss the effects of different types of boundary conditions b c on the linear stability of a solitary wave in a finite length dynamical lattice described by the ablowitz ladik al model types of b c considered are fixed dirichlet no flux neumann and free as well as periodic b c the behaviour of eigenvalues around a stationary nonlinear wave consistent with several types of b c is studied analytically and numerically the translational eigenvalues are found to move away from the origin it is shown that for b c of the fixed type these eigenvalues bifurcate into a neutrally stable oscillatory kind while the no flux and free b c lead to an exponentially weak instability the rotational eigenmodes those related to the gauge invariance of the lattice strictly remain at the origin as gauge invariance is not broken by the linear homogeneous b c these numerical results are compared to the analytical and semi analytical predictions obtained within the approximation of the images generated by the solitary wave beyond the lattice edges a potential effect of continuous spectrum band edge bifurcations on stability is also evaluated with the conclusion that that these bifurcations cannot destabilize the soliton for periodic b c the translational invariance is preserved and so is the lax pair structure sustaining the integrable nature of the problem the al model was chosen so that the effects of boundary conditions are monitored in the absence of non integrable discreteness finally the possibility of the generation of multipulse configurations due to the interplay of finiteness effects with the exponential tail tail interaction of the pulses is examined

existence of solutions for p x laplacian dirichlet problem this paper presents several sufficient conditions for the existence of solutions for the dirichlet problem of p x laplacian div u p x 2 u f x u x u 0 x especially an existence criterion for infinite many pairs of solutions for the problem is obtained the discussion is based on the theory of the spaces lp x and w01 p x

nonuniformly nonlinear elliptic equations of p biharmonic type this paper deals with the existence and multiplicity of weak solutions to nonlinear differential equations involving a general p biharmonic operator in particular p biharmonic operator under dirichlet boundary conditions or navier boundary conditions our method is mainly based on variational arguments

diffusion of protein receptors on a cylindrical dendritic membrane with partially absorbing traps we present a model of protein receptor trafficking within the membrane of a cylin drical dendrite containing small protrusions called spines spines are the locus of most excitatory synapses in the central nervous system and act as localized traps for receptors diffusing within the dendritic membrane we treat the transverse intersection of a spine and dendrite as a spatially extended partially absorbing boundary and use singular perturbation theory to analyze the steady state distribution of receptors we compare the singular perturbation solutions with numerical solutions of the full model and with solutions of a reduced one dimensional model and find good agreement between them all we also derive a system of fokker planck equations from our model and use it to exactly solve a mean first passage time mfpt problem for a single receptor traveling a fixed axial distance along the dendrite this is then used to calculate an effective diffusion coefficient for receptors when spines are uniformly distributed along the length of the cable and to show how a nonuniform distribution of spines gives rise to anomalous subdiffusion

vibrations of thin plates with small clamped patches eigenvalues of fourth order elliptic operators feature prominently in stability analysis of elastic structures this paper considers out of plane modes of vibration of a thin elastic plate perforat

multiple nontrivial solutions for some fourth order semilinear elliptic problems abstract in this paper we consider the existence of multiple nontrivial solutions for some fourth order semilinear elliptic boundary value problems the weak solutions are sought by means of morse theory and local linking

diffusion on a sphere with localized traps mean first passage time eigenvalue asymptotics and fekete points a common scenario in cellular signal transduction is that a diffusing surface bound molecule must arrive at a localized signaling region on the cell membrane before the signaling cascade can be completed the question then arises of how quickly such signaling molecules can arrive at newly formed signaling regions here we attack this problem by calculating asymptotic results for the mean first passage time for a diffusing particle confined to the surface of a sphere in the presence of n partially absorbing traps of small radii the rate at which the small diffusing molecule becomes captured by one of the traps is determined by asymptotically calculating the principal eigenvalue for the laplace operator on the sphere with small localized traps the asymptotic analysis relies on the method of matched asymptotic expansions together with detailed properties of the green s function for the laplacian and the helmholtz operators on the surface of the unit sphere the asymptotic results compare favorably with

hybrid asymptotic numerical approach for estimating first passage time densities of the two dimensional narrow capture problem a hybrid asymptotic numerical method is presented for obtaining an asymptotic estimate for the full probability distribution of capture times of a random walker by multiple small traps located inside a bounded two dimensional domain with a reflecting boundary as motivation for this study we calculate the variance in the capture time of a random walker by a single interior trap and determine this quantity to be comparable in magnitude to the mean this implies that the mean is not necessarily reflective of typical capture times and that the full density must be determined to solve the underlying diffusion equation the method of laplace transforms is used to obtain an elliptic problem of modified helmholtz type in the limit of vanishing trap sizes each trap is represented as a dirac point source that permits the solution of the transform equation to be represented as a superposition of helmholtz green s functions using this solution we construct asymptotic short time solutions of the first passage time density which captures peaks associated with rapid capture by the absorbing traps when numerical evaluation of the helmholtz green s function is employed followed by numerical inversion of the laplace transform the method reproduces the density for larger times we demonstrate the accuracy of our solution technique with a comparison to statistics obtained from a time dependent solution of the diffusion equation and discrete particle simulations in particular we demonstrate that the method is capable of capturing the multimodal behavior in the capture time density that arises when the traps are strategically arranged the hybrid method presented can be applied to scenarios involving both arbitrary domains and trap shapes

the transition to a point constraint in a mixed biharmonic eigenvalue problem the mixed order eigenvalue problem delta delta 2 u delta u lambda u 0 with delta 0 modeling small amplitude vibrations of a thin plate is analyzed in a bounded two dimensional domain omega that contains a single small hole of radius varepsilon centered at some x 0 in omega clamped conditions are imposed on the boundary of omega and on the boundary of the small hole in the limit varepsilon to 0 and for delta mathcal o 1 the limiting problem for u must satisfy the additional point constraint u x 0 0 to determine how the eigenvalues of the laplacian in a domain with a small hole are perturbed by adding the small fourth order term delta delta 2 u together with an additional boundary condition on partial omega and on the hole boundary the asymptotic behavior of the eigenvalues of the mixed order eigenvalue problem are studied in the dual limit varepsilon to 0 and delta to 0 leading order behaviors of eigenvalues are determined for three ranges

brief paper recursive identification for multivariate errors in variables systems the recursive algorithm is given for estimating matrix coefficients of the multivariate errors in variables eiv systems it is shown that under mild conditions the estimate given by the algorithm converges to a limit belonging to the solution set of the yule walker equation satisfied by the true coefficients of the system the sufficient conditions guaranteeing the uniqueness of the solution to the yule walker equation are given in this case the estimate provided by the recursive algorithm is strongly consistent

narrow escape and leakage of brownian particles questions of flux regulation in biological cells raise a renewed interest in the narrow escape problem the determination of a higher order asymptotic expansion of the narrow escape time depends on determining the singularity behavior of the neumann green s function for the laplacian in a three dimensional 3d domain with a dirac mass on the boundary in addition to the usual 3d coulomb singularity this green s function also has an additional weaker logarithmic singularity by calculating the coefficient of this logarithmic singularity we calculate the second term in the asymptotic expansion of the narrow escape time and in the expansion of the principal eigenvalue of the laplace equation with mixed dirichlet neumann boundary conditions with small dirichlet and large neumann parts we also determine the leakage flux of brownian particles that diffuse from a source to an absorbing target on a reflecting boundary of a domain if a small perforation is made in the reflecting boundary

infinitely many solutions for a perturbed nonlinear navier boundary value problem involving the p biharmonic abstract by using critical point theory we establish the existence of infinitely many weak solutions for a class of elliptic navier boundary value problems depending on two parameters and involving the p biharmonic operator

criticality in reactors under domain or external temperature perturbations the conditions for the onset of thermal runaway in reactors with small non uniformities is investigated the reaction is modelled by an arrhenius heat generation term with a finite activation energy and the dimensionless temperature u o is taken to satisfy a nonlinear equation of the form u 0 0f u 0 0 x d vu 0 bu 0 0 x d we investigate three classes of perturbations of this problem first we treat a small temperature variation maintained on the boundary of the domain secondly we consider a small distortion of the boundary of a circular cylindrical domain and thirdly we analyse the effect of a small hole in the domain in each case we derive asymptotic expansions for the critical frank kamenetskii parameter c where is a measure of the size of the perturbation a numerical scheme is then used to determine numerical values for the coefficients in the asymptotic expansion of c finally some of the asymptotic results are compared with corresponding numerical results obtained from a full numerical solution of the perturbed problem

a structure theory for linear dynamic errors in variables models we deal with problems connected with the identification of linear dynamic systems in situations when inputs and outputs may be contaminated by noise the case of uncorrelated noise components and the bounded noise case is considered if also the inputs may be contaminated by noise a number of additional complications in identification arise in particular the underlying system is not uniquely determined from the population second moments of the observations a description of classes of observationally equivalent systems is given continuity properties of mappings relating classes of observationally equivalent systems to the spectral densities of the observations are derived and the classes of spectral densities corresponding to a given maximum number of outputs are studied

composite overlapping meshes for the solution of partial differential equations abstract we discuss the generation of curvilinear composite overlapping grids and the numerical solution of partial differential equations on them a composite overlapping grid consists of a set of curvilinear component grids that cover a region and overlap where they meet continuity conditions interpolation are imposed at the overlapping boundaries the principal advantage of composite grids is in the generation of grids for regions with complicated geometries the grid construction program cmpgrd is used to create composite grids with any number of component grids we describe some techniques for the solution of elliptic and time dependent pdes on composite meshes applications to the solution of the compressible navier stokes equations are presented

least squares identification for armax models without the positive real condition recursive identification problems of linear stochastic feedback control systems described by armax models are studied without imposing the strictly positive real condition on the noise model an increasing lag least squares is used in the first step to estimate the noise process while the parameter estimate is formed in the second step by an extended least squares in the algorithm there is an increase in computational cost in comparison to traditional algorithms however the results of this note do not need any a priori information or conditions on the noise model except that of stability and they are applicable to the identification of general feedback control systems

ground state solutions for singular p laplacian equation in rn abstract in this work we study the ground state solution for the class of singular quasilinear elliptic problem of the form div x a p u p 2 u h x u m 2 u h x u q 2 u x r n where 1 p n a n p p and h r h r 0 we prove the compactly embedding results of the weighted z d a r 1 p r n l h r m r n space of radially symmetric functions and then obtain the existence of nontrivial ground state solution

nonlinearity saturation as a singular perturbation of the nonlinear schroźdinger equation saturation of a kerr type nonlinearity in the nonlinear schro dinger equation nlse can be regarded as a singular perturbation which regularizes the well known blow up phenomenon in the cubic nlse an asymptotic expansion is proposed which takes into account multiple scale behavior both in the longitudinal and transverse directions in one dimension this leads to a free boundary problem reduction where the solitary wave acts solely to reflect impinging waves and is accelerated by an elastic transfer of momentum in two dimensions we find that interaction of a solitary wave and an adjacent wave field is governed by behavior of certain eigenfunctions of the linearized fast scale operator this leads to an outer solution with a free logarithmic singularity whose position evolves by virtue of a large transfer of momentum between the ambient and solitary waves however for a certain value of wave power we find there is essentially no interaction and the solitary wave is asymptotically transparent to the ambient field we test our results by numerical simulation of both the full equation and free boundary reductions

paper identification of scalar errors in variables models with dynamics the paper considers the task of identifying a causal linear dynamic system excited by stationary gaussian zero mean noise of unknown spectrum and given measurements of the system input and output contaminated by independent additive stationary noise signals of unknown spectra while the solution is normally not unique finite dimensional parameterizations of the solution set are given in some cases involving just one parameter even though the various spectra may not be rational

the narrow escape problem the narrow escape problem in diffusion theory is to calculate the mean first passage time of a diffusion process to a small target on the reflecting boundary of a bounded domain the problem is equivalent to solving the mixed dirichlet neumann boundary value problem for the poisson equation with small dirichlet and large neumann parts the mixed boundary value problem which goes back to lord rayleigh originates in the theory of sound and is closely connected to the eigenvalue problem for the mixed problem and for the neumann problem in domains with bottlenecks we review here recent developments in the non standard asymptotics of the problem which are based on several ingredients a better resolution of the singularity of neumann s function resolution of the boundary layer near the small target by conformal mappings of domains with bottlenecks and the breakup of composite domains into simpler components the new methodology applies to two and higher dimensional problems selected applications are r

sign changing solutions for p biharmonic equations with hardy potential in the half space abstract in this paper by using the method of invariant sets of descending flow we obtain the existence of positive solutions and sign changing solutions of p biharmonic equations with hardy potential in the half space

existence of solutions for a class of noncooperative elliptic systems we establish the existence of a nontrivial solution for a class of noncooperative elliptic systems with nonlinearities of superlinear growth moreover if there is resonance we also find at least a solution all results are obtained by the minimax methods in critical point theory

mountain pass solutions to equations of p laplacian type abstract this work is devoted to study the existence of solutions to equations of p laplacian type we prove the existence of at least one solution and under further assumptions the existence of infinitely many solutions in order to apply mountain pass results we introduce a notion of uniformly convex functional that generalizes the notion of uniformly convex norm

three solutions for a navier boundary value problem involving the p biharmonic the existence of at least three weak solutions is established for a class of navier boundary value problem involving the p biharmonic our technical approach is based on the three critical points theorem obtained by b ricceri

non differentiable functionals and applications to elliptic problems with discontinuous nonlinearities abstract multiple critical points theorems for non differentiable functionals are established applications both to elliptic variational hemivariational inequalities and eigenvalue problems with discontinuous nonlinearities are then presented

stochastic system identification with noisy input using cumulant statistics addresses the problem of estimating the parameters of stochastic linear systems when the measurements of the system input as well as the system output are noise contaminated it is assumed that the input is non gaussian and the noises are gaussian the square root of the magnitude of the fourth cumulant of a generalized error signal is proposed as a performance criterion for parameter estimation an optimization algorithm is presented strong consistency of the proposed parameter estimators is proved under certain sufficient conditions both single input single output and multiple input multiple output cases are investigated finally simulation results are presented to illustrate the proposed approach

the dynamics and pinning of a spike for a reaction diffusion system the motion of a one spike solution to a simplified form of the gierer meinhardt activator inhibitor model is studied in both a one dimensional and a two dimensional domain the pinning effect on the spike motion associated with the presence of spatially varying coefficients in the differential operator referred to as precursor gradients is studied in detail in the one dimensional case we derive a differential equation for the trajectory of the spike in the limit e 0 where e is the activator diffusivity a similar differential equation is derived for the two dimensional problem in the limit for which e 1 and d 1 where d is the inhibitor diffusivity a numerical finite element method is presented to track the motion of the spike for the full problem in both one and two dimensions finally the numerical results for the spike motion are compared with corresponding asymptotic results for various examples

properties of the principal eigenvalues of a general class of non classical mixed boundary value problems in this paper we characterize the existence of principal eigenvalues for a general class of linear weighted second order elliptic boundary value problems subject to a very general class of mixed boundary conditions our theory is a substantial extension of the classical theory by p hess and t kato 1980 comm partial differential equations5 999 1030 in obtaining our main results we must give a number of new results on the continuous dependence of the principal eigenvalue of a second order linear elliptic boundary value problem with respect to the underlying domain and the boundary condition itself these auxiliary results complement and in some sense complete the theory of d daners and e n dancer 1997 j differential equations138 86 132 the main technical tool used throughout this paper is a very recent characterization of the strong maximum principle in terms of the existence of a positive strict supersolution due to h amann and j lopez gomez 1998 j differential equations146 336 374

multiple solutions for p laplacian type equations abstract in this paper we establish the existence of three weak solutions of an equation which involves a general elliptic operator in divergence form in particular a p laplacian operator while the nonlinearity has a p 1 sublinear growth at infinity this result completes some recent papers where mountain pass type solutions were obtained providing the nonlinear term via a p 1 superlinear growth at infinity fulfilling an ambrosetti rabinowitz type condition in our case an abstract critical point result is applied proved by g bonanno g bonanno some remarks on a three critical points theorem nonlinear analysis 54 2003 651 665