eigenvalue problems for anisotropic elliptic equations an orlicz sobolev space setting abstract the paper studies a class of anisotropic eigenvalue problems involving an elliptic nonhomogeneous differential operator on a bounded domain from r n with a smooth boundary some results regarding the existence or non existence of eigenvalues are obtained in each case the competition between the growth rates of the anisotropic coefficients plays an essential role in the description of the set of eigenvalues

on variational inequalities with maximal monotone operators and multivalued perturbing terms in sobolev spaces with variable exponents abstract we are concerned in this paper with variational inequalities of the form a u v u f u v u l v u v k u k where a is a maximal monotone operator f is an integral multivalued lower order term and k is a closed convex set in a sobolev space of variable exponent we study both coercive and noncoercive inequalities in the noncoercive case a sub supersolution approach is followed to obtain the existence and some other qualitative properties of solutions between sub and supersolutions

robust stability of an interval plant with respect to a convex region in the complex plane the determination of robust stability of interval polynomials with respect to an arbitrary closed convex contour in the left half complex plane is considered it is shown that the problem can be solved by checking only the root locations of a subset of the exposed edges of the family the number of exposed edges to be checked depends on the damping margin defined by the contour and the degree of interval polynomials but does not depend on the exact shape of the contour a simple easy to apply graphical approach determines the subset of the exposed edges an example illustrates the merit of the approach

eigenvalues of p x laplacian dirichlet problem abstract this paper studies the eigenvalues of the p x laplacian dirichlet problem div u p x 2 u u p x 2 u in u 0 on where is a bounded domain in rn and p x is a continuous function on such that p x 1 we show that the set of eigenvalues is a nonempty infinite set such that sup we present some sufficient conditions for inf 0 and for inf 0 respectively

existence and multiplicity of solutions for quasilinear nonhomogeneous problems an orlicz sobolev space setting abstract we study the boundary value problem div log 1 u q u p 2 u f u in u 0 on where is a bounded domain in r n with smooth boundary we distinguish the cases where either f u u p 2 u u r 2 u or f u u p 2 u u r 2 u with p q 1 p q min n r and r n p n p n p in the first case we show the existence of infinitely many weak solutions for any 0 in the second case we prove the existence of a nontrivial weak solution if is sufficiently large our approach relies on adequate variational methods in orlicz sobolev spaces

on a sub supersolution method for variational inequalities with leray lions operators in variable exponent spaces abstract in this paper we consider a sub supersolution method for variational inequalities with leray lions operators in sobolev spaces with variable exponents existence and qualitative properties of solutions between sub and supersolutions are established

regularity results for a class of functionals with non standard growth we consider the integral functional under non standard growth assumptions that we call p x type namely we assume that a relevant model case being the functional under sharp assumptions on the continuous function p x 1 we prove regularity of minimizers energies exhibiting this growth appear in several models from mathematical physics

a multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids the goal of this correction is to correct a mistake that appears in the proof of both lemma 3 9 and 3 10 in the article mih ilescu r dulescu 2006 1 the mistake in the proof of lemma 3 9 and 3 10 is mainly owing to the fact that we wrongly computed the expression of function g x t

a minimax inequality and its applications to ordinary differential equations the aim of this paper is to investigate the minimax inequality which plays a fundamental role in the critical points theorem of b ricceri below equivalent formulations are shown and characterization is proved in particular for a special class of functionals as an application a multiplicity result for an ordinary dirichlet problem is emphasized

multiple solutions for a nonhomogeneous dirichlet problem in orlicz sobolev spaces abstract in this paper moving within the framework of orlicz sobolev spaces we guarantee through variational arguments the existence of three weak solutions to the nonhomogeneous boundary value problem div a u x u x f x u g x u in u 0 on with bounded domain in r n with smooth boundary real parameters f g r r caratheodory functions and the function t a t t odd increasing homeomorphism from r onto r applications and comparisons are also presented in particular we improve a result for an eigenvalue problem established by mih ilescu and repovs in 15

comments on comments on stability analysis of a family of matrices by j h kim and z bien a flaw is pointed out in the proof of a necessary and sufficient condition for robust stability of a polytope of matrices given by j h kim and z bien ibid vol 387 no 9 pp 1470 1472 sep 1992 in their comments on a paper by the present authors ibid vol 35 no 11 pp 1257 1259 nov 1190 hence the necessary condition as proposed may not be correct

structured and simultaneous lyapunov functions for system stability problems abstract it is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic lyapunov function of a certain structure which establishes stability of x ax for some appropriate a the existence of such a lyapunov function can be determined by solving a convex program we present several numerical methods for these optimization problems a simple numerical example is given

multiplicity results for a neumann problem involving the p laplacian abstract in this paper we establish some multiplicity results for the following neumann problem div u p 2 u x u p 2 u x f u in u 0 on the multiple solutions are obtained by combining an existence theorem recently proved by g anello and g cordaro with well known critical point theorems

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

multiple solutions for a neumann system involving subquadratic nonlinearities abstract in this paper we consider the model semilinear neumann system n u a x u c x f u u v in v b x v c x f v u v in u v 0 on where r n is a smooth open bounded domain denotes the outward unit normal to 0 is a parameter a b c l 0 and f c 1 r 2 r 0 is a nonnegative function which is subquadratic at infinity two nearby numbers are determined in explicit forms and with 0 such that for every 0 system n has only the trivial pair of solution while for every system n has at least two distinct nonzero pairs of solutions

perturbed kirchhoff type neumann problems in orlicz sobolev spaces the aim of this paper is to establish the existence of infinitely many solutions for perturbed kirchhoff type non homogeneous neumann problems involving two parameters to be precise we prove that an appropriate oscillating behaviour of the nonlinear term even under small perturbations ensures the existence of infinitely many solutions our approach is based on recent variational methods for smooth functionals defined on orlicz sobolev spaces

quasilinear elliptic non homogeneous dirichlet problems through orlicz sobolev spaces abstract in this paper we are interested in the existence of infinitely many weak solutions for a non homogeneous eigenvalue dirichlet problem by using variational methods in an appropriate orlicz sobolev setting we determine intervals of parameters such that our problem admits either a sequence of non negative weak solutions strongly converging to zero provided that the non linearity has a suitable behaviour at zero or an unbounded sequence of non negative weak solutions if a similar behaviour occurs at infinity

eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent in this paper we are concerned with a new class of anisotropic quasilinear elliptic equations with a power like variable reaction term one of the main features of our work is that the differential operator involves partial derivatives with different variable exponents so that the functional analytic framework relies upon anisotropic sobolev and lebesgue spaces existence and nonexistence results are deeply influenced by the competition between the growth rates of the anisotropic coefficients our main results point out some striking phenomena related to the existence of a continuous spectrum in several distinct situations

harmonic type approximation lemmas we give a survey of known and not known harmonic type approximation lemmas which are descendants of the classical de giorgi s one and we outline some of their recent or possible applications

the number of solutions for a class of nonlocal nonhomogeneous gradient operator equations abstract this paper deals with the number of solutions for a class of nonlocal nonhomogeneous gradient operator equations of the form a i u i u f where i c 1 x r x is a reflexive banach space i 0 0 i is even and strictly convex i u u as u i x x is a bounded homeomorphism but is not necessarily homogeneous a 0 r is continuous f x 0 some properties and examples of such a functional i are given some results on the number of solutions of the nonlocal equation are obtained

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

solutions for neumann boundary value problems involving p x laplace operators abstract in this paper we study the nonlinear neumann boundary value problem of the following form p div u p x 2 u u p x 2 u f x u in u p x 2 u g x u on using the variational method under appropriate assumptions on f and g we obtain a number of results on existence and multiplicity of solutions also what is also interesting is that we obtain some results which can be considered as extensions of the classical result named combined effects of concave and convex nonlinearities moreover the positive solution of the problem is considered

an existence result for a class of pp laplacian elliptic systems involving homogeneous nonlinearities in rn abstract in the present paper we study the existence of nontrivial solutions for a class of p laplacian elliptic systems in r n a new existence result for nontrivial solutions is obtained by means of variational methods

two non trivial solutions for a non homogeneous neumann problem an orlicz sobolev space setting in this paper we study a non homogeneous neumann type problem which involves a nonlinearity satisfying a non standard growth condition by using a recent variational principle of ricceri we establish the existence of at least two non trivial solutions in an appropriate orlicz sobolev space

mountain pass and ekeland s principle for eigenvalue problem with variable exponent in this article we study the boundary value problem div u p x 2 u u x 2 u u q x 2 u in u 0 on where is a smooth bounded domain in n and p q are continuous functions on we show that for any 0 there exists infinitely many weak solutions respectively if 0 and small enough then there exists a non negative non trivial weak solution our approach relies on the variable exponent theory of generalized lebesgue sobolev spaces combined with a 2 symmetric version for even functionals of the mountain pass theorem respectively on simple variational arguments based on ekeland s variational principle this article is devoted to the special issue vaxjo conference 2008

existence of three solutions for p q biharmonic systems abstract in this paper we establish the existence of at least three solutions to a navier boundary problem involving the p q biharmonic systems the technical approach is mainly based on a three critical points theorem of b ricceri

the prediction approach to robust variance estimation in two stage cluster sampling abstract robust statistics are derived for estimating the error variance when a finite population total or a ratio of totals is estimated from a two stage cluster sample in which the first stage sampling fraction is small the analysis is based on prediction superpopulation models that allow for very general correlation structure within clusters results are obtained for when all cluster sizes are known and for when sizes are known only for sample clusters ratio regression and mean of ratios statistics are in the class of population total estimators considered

a general variational principle and some of its applications abstract in this paper given a reflexive real banach space x and two sequentially weakly lower semicontinuous functionals on x with strongly continuous and coercive we are mainly interested in the existence of infinitely many local minima of the functional for each sufficiently large r

poststratification and conditional variance estimation poststratification estimation is a technique used in sample surveys to improve efficiency of estimators survey weights are adjusted to force the estimated numbers of units in each of a set of estimation cells to be equal to known population totals the resulting weights are then used in forming estimates of means or totals of variables collected in the survey for example in a household survey the estimation cells may be based on age race sex categories of individuals and the known totals may come from the most recent population census although the variance of a poststratified estimator can be computed over all possible sample configurations inferences made conditionally on the achieved sample configuration are desirable theory and a simulation study using data from the u s current population survey are presented to study both the conditional bias and variance of the poststratified estimator of a total the linearization balanced repeated replication and jackknife variance estimators are also exa

existence results for nonlinear elliptic equations with leray lions operator and dependence on the gradient the existence of positive solutions for nonlinear elliptic problems under dirichlet boundary condition is studied as well as the compactness and directness of the solution set the main novelties consist in the presence of a leray lions operator in the differential part and in the dependence of the reaction term on the gradient of the solution our approach relies on the method of sub supersolution nonlinear regularity theory and strong maximum principle

generalized variance functions in stratified two stage sampling abstract generalized variance functions gvf s are used in a number of sample surveys as a convenient method of publishing sampling errors the method consists of estimating the relative variance relvariance of an estimator of a total t by using a model with the form a b t using the prediction approach to finite population sampling some asymptotic theory is presented for estimators of totals that are linear combinations of sample cluster means from stratified two stage cluster samples one choice of gvf estimator is shown to be consistent under a particular class of prediction models the theory is illustrated by an empirical study in which two stage stratified samples are selected from a population of households the prediction model is one in which units within a stratum have a common mean and variance units in the same cluster are correlated but units in different clusters are not and in which the common variance is a quadratic function of the common mean in a stratum bernoulli and poisson r

solutions for p x laplacian dirichlet problems with singular coefficients using the critical point theory we investigate the existence and multiplicity of solutions for p x laplacian dirichlet problem with singular coefficients

existence of three solutions for a non homogeneous neumann problem through orlicz sobolev spaces abstract the aim of this paper is to establish a multiplicity result for an eigenvalue non homogeneous neumann problem which involves a nonlinearity fulfilling a nonstandard growth condition precisely a recent critical points result for differentiable functionals is exploited in order to prove the existence of a determined open interval of positive eigenvalues for which the problem admits at least three weak solutions in an appropriate orlicz sobolev space

robust stability of control systems with polytopical uncertainty a nyquist approach for technical plants a bounded continuum of parameter values describes admissible process models a robust controller guarantees the observance of minimal requirements for all of the allowed process models in this paper a frequency domain approach is proposed that permits the instability of a family of polynomials to be checked this method can be extended in an easy manner to investigate the instability of a closed loop the plant is thereby described by a family of models with a polytopical region of uncertainty in the parameter space as an important special case of the general d stability the hurwitz stability of the closed loop is investigated and a minimal set of necessary and sufficient conditions for robust hurwitz stability is given a generalization for other stability domains is possible besides an algebraic criterion based on a zero inclusion check for a minimal set of exposed edges of the polytopical region a graphic criterion of nyquist type can also be used

on a nonlinear eigenvalue problem in orliczsobolev spaces we consider the eigenvalue problem in an arbitrary orliczsobolev space we show that the existence of an eigenvalue can be derived from a generalized version of lagrange multiplier rule our approach also applies to more general problems we emphasize that no 2 condition is imposed

multiple solutions for a nonlinear and non homogeneous problem in orlicz sobolev spaces abstract we study a non homogeneous boundary value problem in a smooth bounded domain in r n we prove the existence of at least two non negative and non trivial weak solutions our approach relies on orlicz sobolev spaces theory combined with adequate variational methods and a variant of mountain pass lemma

stability analysis of a family of matrices the authors extend the use of the lyapunov equation method to check the stability of a family of matrices the family of interval matrices is defined as the convex hull of a finite number of matrices and is a special case where each element has independent perturbation while the stability of interval matrices cannot be inferred from the stability of its vertex matrices the authors show that the family of matrices will be stable if the symmetric matrices associated with the vertex matrices have matrix measures less than two

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

a result on elliptic systems with neumann conditions via ricceri s three critical points theorem abstract this paper is concerned with the study of the existence of nontrivial solutions for elliptic systems involving the p laplacian by using the result of b ricceri a three critical points theorem revisited nonlinear anal 2008 in press doi 10 1016 j na 2008 04 010 we establish the existence of at least three solutions

gradient estimates for the p x laplacean system we prove calderon and zygmund type estimates for a class of elliptic problems whose model is the non homogeneous p x laplacean system div jduj p x 2 du div jf j p x 2 f

existence of solutions for p x laplacian problems on a bounded domain in this paper we study the following p x laplacian problem div a x vd uv p x 2 d u b x v uv p x 2 u f x u x e u u 0 on p u where 1 p 1 l p x l p 2 n u s r n is a bounded domain and applying the mountain pass theorem we obtain the existence of solutions in w 0 1 p x for the p x laplacian problems in the superlinear and sublinear cases 2004 elsevier inc all rights reserved

differential equations of divergence form in musielak sobolev spaces and a sub supersolution method abstract we study some properties of differential operators of divergence form in musielak sobolev spaces and establish a sub supersolution method for differential equations of divergence form with homogeneous neumann or dirichlet boundary condition in musielak sobolev spaces

existence of periodic solutions for ordinary differential systems in musielak orlicz sobolev spaces abstract in this paper we study the periodic solutions for the ordinary differential systems in musielak orlicz sobolev spaces we get some propositions of the musielak orlicz sobolev space w t 1 which are used to get the existence results using variational methods we have some existence results of the periodic solutions for the ordinary differential systems in musielak orlicz sobolev spaces