on a class of hemivariational inequalities at resonance abstract we consider a class of noncoercive hemivariational inequalities involving the p laplacian at resonance we use the unilateral growth condition so the energy functional is nonsmooth nonconvex and its effective domain does not coincide with the whole space w 1 p 0 to avoid this difficulty we study the problem in finite dimensional spaces using the mountain pass theorem for locally lipschitz functionals and then we pass to the limit to obtain the existence of solutions

comparison and stability of solutions to a class of quasilinear parabolic problems on presente des resultats de comparaison et d unicite pour les solutions de problemes aux valeurs limites quasilineaires paraboliques avec et sans obstacles un resultat de stabilite dans l 1 donne la stabilisation asymptotique dans cet espace quand t vers le probleme elliptique correspondant

solvability of nonlinear variational hemivariational inequalities abstract in this paper we study nonlinear elliptic differential equations driven by the p laplacian with unilateral constraints produced by the combined effects of a monotone term and of a nonmonotone term variational hemivariational inequality our approach is variational and uses the subdifferential theory of nonsmooth functions and the theory of accretive and monotone operators also using these ideas and a special choice of the monotone term we prove the existence of a strictly positive smooth solution for a class of nonlinear equations with nonsmooth potential hemivariational inequality

an investigation of the small slope approximation for scattering from rough surfaces part i theory the small slope approximation ssa of voronovich sov phys jetp 62 65 70 1985 is a promising method for application to scattering from many natural surfaces the theory gives a systematic expansion that can be interpreted as a series in generalized surface slope the ssa series for the t matrix satisfies the appropriate reciprocity condition at each order and reduces to the standard perturbation series for small surface roughness in this paper we examine in detail the derivation of the ssa for surfaces subject to the dirichlet zero field boundary condition a number of points are discussed including the requirements for determining the series terms in addition questions have been raised recently about the ssa it has been argued that 1 an assumption in the derivation contradicts the exact formulation of the problem and 2 there is an arbitrariness in determining the series terms these two points are refuted and the assumptions needed to determine the series terms unambiguously are clarified the meaning of slope orders in the ssa series expansion are examined and the concept of generalized slope is discussed a future companion paper part ii numerical studies will present an investigation of the accuracy of the ssa through comparison with exact results

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

on a comparison principle for delay coupled systems with nonlocal and nonlinear boundary conditions abstract this paper is concerned with delay coupled systems of parabolic equations with nonlocal and nonlinear boundary conditions for them a new and general comparison principle is established which is more general and useful than the existing results

analysis and control of differential inclusions with anti periodic conditions we deal with the optimal control of systems driven by differential inclusions with anti periodic conditions in banach spaces the operators in the differential inclusions describing the control system all depend on control variables by a solution of the control system we mean a trajectory control pair we first prove that for fixed control variables the set of solutions is non empty for the corresponding differential inclusion with anti periodic conditions we then show the functional topological properties of the set of solutions finally we investigate the existence of solutions to the optimal control problem these abstract results can be used to study optimal control systems of evolutionary hemi variational inequalities

a variational like inequality for multifunctions with applications abstract we study a variational like inequality problem for a multifunction a certain relevant complementarity problem is defined we establish some existence theorems for the above two problems an application to convex mathematical programming is also shown

auxiliary principle and iterative algorithms for generalized set valued strongly nonlinear mixed variational like inequalities in this paper we extend the auxiliary principle technique to study a class of generalized set valued strongly nonlinear mixed variational like inequalities we prove the existence of a solution of the auxiliary problem for the generalized set valued strongly nonlinear mixed variational like inequalities construct the iterative algorithm for the generalized set valued strongly nonlinear mixed variational like inequalities and show the existence of a solution of the generalized set valued strongly nonlinear mixed variational like inequality by using the auxiliary principle technique we also prove the convergence of iterative sequences generated by the algorithm

noncoercive variational inequalities some applications ever since the fundamental paper of lions and stampacchia io the subject of variational inequalities has become a very active area of study and become an important tool in the study of nonlinear partial differential equations which are subject to various types of constraints see e g l 5 8 111 in lo the authors consider first the case of coercive forms and then using elliptic regularization problems involving noncoercive but nonnegative forms we shall use a similar approach to study variational inequalities involving noncoercive bilinear forms and nonlinear functionals which are nice perturbations of lower semi continuous convex functionals furthermore our bilinear forms need not necessarily have a finite dimensional kernel our investigation has been motivated by some work of baiocchi gastaldi and tomarelli see 3 61 where variational inequalities involving so called compact coercive bilinear forms are studied we shall introduce here a somewhat more general concept that of a p coercive bilinear form and study variational inequalities involving such forms and nonlinear functionals which are compact and bounded perturbations of lower semi continuous convex functionals in the next section we shall introduce the necessary terminology prove some preliminary results and give the statement of the abstract problem we then shall state and prove our main abstract result and conclude the paper with applications including one to the study of a flat plate on an elastic foundation with unilateral boundary conditions see e g l for the terminology and one to the study of unilateral problems in semipermeable media see 5

nonlinear evolution equations with nonmonotonic perturbations soit v un espace de banach reflexif densement et continument plonge dans un espace de hilbert reel h on considere l existence des solutions du probleme aux valeurs initiales du dt au g u f 0 t t u 0 u 0 ou a est un operateur monotone de v dans v g v h est une application continue et f 0 t v est une fonction mesurable

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

on variational and quasi variational inequalities with multivalued lower order terms and convex functionals abstract in this paper we consider the existence and some qualitative properties of solutions of variational inequalities of the form find u d j a u v u f u v u j v j u 0 v x and of quasi variational inequalities of the form find u d j u a u v u f u v u j u v j u u 0 v x where a is a second order elliptic operator of leray lions type f is a multivalued lower order term j and j u are convex functionals and j u also depends on u we concentrate here in noncoercive cases and use sub supersolution methods to study the existence and enclosure of solutions and also the existence of extremal solutions between sub and supersolutions

quasilinear elliptic inclusions of hemivariational type extremality and compactness of the solution set abstract we consider the dirichlet boundary value problem for an elliptic inclusion governed by a quasilinear elliptic operator of leray lions type and a multivalued term which is given by the difference of clarke s generalized gradient of some locally lipschitz function and the subdifferential of some convex function problems of this kind arise e g in mechanical models described by nonconvex and nonsmooth energy functionals that result from nonmonotone multivalued constitutive laws our main goal is to characterize the solution set of the problem under consideration in particular we are going to prove that the solution set possesses extremal elements with respect to the underlying natural partial ordering of functions and that the solution set is compact the main tools used in the proofs are abstract results on pseudomonotone operators truncation and special test function techniques zorn s lemma as well as tools from nonsmooth analysis

boundary hemivariational inequality of parabolic type abstract in this paper we consider a parabolic hemivariational inequality with a nonmonotone multivalued boundary condition and with a time dependent pseudomonotone operator we establish the existence of solutions for such inequality our proof is based on a known surjectivity result for operators of pseudomonotone type we present an example of semipermeability heat conduction problem to which the result applies

existence results for quasilinear parabolic hemivariational inequalities abstract this paper is devoted to the periodic problem for quasilinear parabolic hemivariational inequalities at resonance as well as at nonresonance by use of the theory of multi valued pseudomonotone operators the notion of generalized gradient of clarke and the property of the first eigenfunction we build a landesman lazer theory in the nonsmooth framework of quasilinear parabolic hemivariational inequalities

sub super solution method for a class of higher order evolution hemivariational inequalities abstract in this paper we extend the extremality results for the variational inequality to a higher order evolution hemivariational inequality more precisely we give an existence theorem of solution for the higher order evolution hemivariational inequality by using the sub super solution method we prove the compactness of the solution set within an order interval formed by the sub solution and super solution we also show an existence theorem of the extremal solution for the higher order evolution hemivariational inequality under consideration

oscillations of delay difference systems this paper is concerned with the oscillatory behavior of a linear difference system either autonomous or nonautonomous criteria for oscillations are obtained in a way that is either dependent on or independent of the delays the structure of the family of delays for which the system exhibits an oscillatory behavior is also analyzed

positive solutions of variational inequalities a degree theoretic approach if the mapping a is strictly monotone and coercive is equivalent to a fixed point equation u m u in k cf section 1 suppose that m is continuous and maps bounded subsets of k into compact ones then due to the fact that k is a retract of x it is possible to define a fixed point index of m with properties similar to those associated with the leray schauder degree 1 sect 111 in section 1 we introduce another index which is based on the previous one but has the advantage of being directly related to inequality rather than to the fixed point equation u m u in section 2 we apply this new index in order to show that if c is a closed convex subset of k then under suitable assumptions upon f the set of solutions of the inequality

coercive and semicoercive hemivariational inequalities variational inequalities have a concrete mechanical meaning they are expressions of the principle of virtual work or power in its inequality form in the case of lack of monotonicity of the underlying stress strain or reaction displacement conditions or equivalently if the corresponding energy functionals are nonconvex the variational expressions are no longer variational inequalities another type of inequality expression arises as variational formulation of the problem these expressions have been introduced in mechanics by the author and are called hemivariational inequalities the aim of this paper is the formulation of an abstract mathematical theory for coercive and semicoercive hemivariational inequalities

existence of solutions for hyperbolic hemivariational inequalities in this paper we study a hyperbolic hemivariational inequality with a nonlinear pseudomonotone operator depending on the derivative of an unknown function and a linear monotone operator depending on an unknown function using the surjectivity result for l pseudomonotone operators an existence result for such inequalities is proved

boundary hemivariational inequality problems with doubly nonlinear operators in this paper we investigate a class of nonlinear boundary hemivariational inequality problems under suitable hypotheses the existence of solutions is established via rewriting these problems into a class of evolution inclusions and using the discretization method and the theory of pseudomonotone operators moreover the continuous dependence result of the solutions to the initial data is given

existence and regularity results for doubly nonlinear inclusions with nonmonotone perturbation abstract this paper deals with a class of nonlinear evolution inclusions arising from enthalpy formulation of heat conduction problems with phase change and nonmonotone source using time discretization technique and monotone operators theory we show the existence of weak solutions then we prove strong convergence of approximate solutions and lift regularity of the weak solutions under appropriate conditions moreover application to physical model described by hemivariational inequality is given

iterative algorithm for completely generalized set valued strongly nonlinear mixed variational like inequalities a class of completely generalized set valued strongly nonlinear mixed variational likeinequalities is introduced the auxiliary principle technique is extended to study this new class of mixed variational like inequalities the existence of a solution of the auxiliary problem for this new class of mixed variational like inequalities is shown the iterative algorithm for this new class of mixed variational like inequalities is given by virtue of this existence result moreover the existence of a solution of this new class of mixed variational like inequalities and the strong convergence of iterative sequences generated by the algorithm are shown the convergence criteria are different from some early and recent ones presented in the literature

oscillations of differential difference systems of neutral type this note is concerned with the oscillatory behavior of a linear differential difference system of neutral type criteria for oscillations are obtained for autonomous and nonautonomous systems

optimal control of feedback control systems governed by hemivariational inequalities this paper is mainly concerned with the feedback control systems governed by evolution hemivariational inequalities by using the properties of multimaps and clarke s subdifferential we formulate some sufficient conditions to guarantee the existence result of feasible pairs of the feedback control systems we also present an existence result of optimal control pairs for an optimal control problem we emphasize that our results cannot be obtained straightforwardly from the previous works

existence of solutions for quasilinear elliptic obstacle problems two existence results for a class of obstacle problems are obtained by using a result developed in this paper

an obstacle problem for nonlinear hemivariational inequalities at resonance in this paper we examine an obstacle problem for a nonlinear hemivariational inequality at resonance driven by the p laplacian using a variational approach based on the nonsmooth critical point theory for locally lipschitz functionals defined on a closed convex set we prove two existence theorems in the second theorem we have a pointwise interpretation of the obstacle problem assuming in addition that the obstacle is also a kind of lower solution for the nonlinear elliptic differential inclusion

monotone penalty approximation of extremal solutions for quasilinear noncoercive variational inequalities abstract this paper is about a monotone approximation scheme for extremal least or greatest solutions of the following variational inequality u k au f u v u 0 v k in the interval between some appropriately defined sub and supersolutions the variational inequality is approximated by a sequence of penalty equations the extremal solutions of the penalty equations constructed iteratively and forming a monotone sequence are proved to converge to the corresponding solutions of the original inequality we note that no monotoneity assumption on the lower order term f is imposed

fixed point theory and nonlinear problems introduction among the most original and far reaching of the contributions made by henri poincare to mathematics was his introduction of the use of topological or qualitative methods in the study of nonlinear problems in analysis his starting point was the study of the differential equations of celestial mechanics and in particular of their periodic solutions his work on this topic began with his thesis in 1879 and was developed in detail in his great three volume work methodes nouvelles de la mechanique celeste which appeared in the early 1890s and summarized his many memoirs of the intervening period it continued until his memoir shortly before his death in 1912 in which he put forward the unproved fixed point result usually referred to as poincare s last geometric theorem the ideas introduced by poincare include the use of fixed point theorems the continuation method and the general concept of global analysis the writer s acquaintance with poincare s influence came through contact with solomon lefschetz and marston morse both of whom were very explicit as to the role of poincare as an initiator in this direction of mathematical development in 1934 in the foreword to his colloquium volume on the calculus of variations in the large morse had put this forward very forcefully in the first paragraph

the validity of the perturbation approximation for rough surface scattering using a gaussian roughness spectrum the validity of the perturbation approximation for rough surface scattering is examined 1 by comparison with exact results obtained by solving an integral equation and 2 through comparison of low order perturbation predictions with higher order predictions the pressure release boundary condition is assumed and the field quantity calculated is the bistatic scattering cross section a gaussian roughness spectrum is used and the surfaces have height variations in only one direction it is found in general that the condition kh 1 k is the acoustic wavenumber h is the rms surface height is insufficient to guarantee the accuracy of first order or higher order perturbation theory when the surface correlation length l becomes too large or too small with h held fixed higher order perturbation terms can make larger contributions to the scattering cross section than lower order terms an explanation for this result is given the regions of validity for low order perturbation theory are also given th

on existence of solutions for parabolic hemivariational inequalities abstract a class of parabolic hemivariational inequalities is considered in which the energy function is locally lipschitz not necessarily convex or differentiable and the nonlinear evolution operator is multivalued and generalized pseudomonotone using techniques of multivalued analysis and a surjectivity result for l generalized pseudomonotone operators we prove the existence for a cauchy problem and a periodic problem some applications to nonsmooth mechanics are also indicated

on the bang bang principle for nonlinear evolution hemivariational inequalities control systems abstract the purpose of this paper is to discuss the control systems of nonlinear evolution hemivariational inequalities and their bang bang principle in banach space at first we show that extremal trajectories are in fact dense in the trajectories of the original system with convexified feedback control second by using the density results the nonlinear and infinite dimensional versions of the bang bang principle for hemivariational inequalities control systems is derived in the end an example is provided to illustrate the application of the obtained theory

existence of solutions for wave type hemivariational inequalities with noncoercive viscosity damping abstract in this paper we prove the existence of solutions for a hyperbolic hemivariational inequality of the form u au bu j u f where b is a linear elliptic operator and a is linear and nonnegative not necessarily coercive

electromagnetic scattering from perfectly conducting rough surfaces a new full wave method a method that does not make use of the telegraphist s equations and takes into account the two dimensional roughness of the surface from the start is developed it is shown that the scattering coefficients obtained agree with those given in earlier work by e bahar 1973 1987 the method is based on reducing the three dimensional scattering problem to a two dimensional problem by expanding each rectangular component of maxwell s equations in terms of local basis functions along the perpendicular direction to the mean surface the transformed two dimensional field equations are solved using fourier transforms the full wave solutions are also compared with the first order perturbation solutions the kirchhoff type solutions and integral equation results

a comparison of forward boundary integral and parabolic wave equation propagation models the parabolic wave equation and its variants have provided the theoretical framework for most practical forward propagation models split step integration generates an easily obtained robust solution for most applications irregular boundaries can be incorporated by using a conformal mapping technique introduced by beilis and tappert 1979 and refined by donohue and kuttler see ibid vol 48 p 260 77 2000 in an earlier paper we demonstrated an alternative method that incorporates a numerical solution to the forward boundary integral equation within each split step cycle this paper compares predictions of forward propagation obtained by these two distinctly different methods the results confirm that the pwe based method is very accurate for smoothly varying surfaces and that it captures the primary forward structure even in the presence of unresolved surface detail the moderate loss of fidelity is often an acceptable trade for increased computational efficiency there are situations however where the details of the surface structure are important furthermore the induced surface currents are unique to the forward boundary integral method we illustrate their use by calculating the bistatic scatter that would he measured from an isolated surface segment we show that the scattered field measured in this way can be normalized to form a bistatic scatter function only when the illuminating beam is tilted slightly toward the surface we interpret this disparity as a breakdown in concept that underlies a local scattering function

enclosure results for quasilinear systems of variational inequalities abstract in this paper we consider systems of quasilinear elliptic variational inequalities and prove the existence of minimal and maximal in the set theoretical sense solutions within some ordered interval of an appropriately defined pair of sub and supersolutions we show that the notion of sub and supersolutions of variational inequalities introduced here is consistent with the usual notion of sub supersolutions for variational equations for weakly coupled quasimonotone systems of variational inequalities the existence of smallest and greatest solutions is proved

on some elliptic hemivariational and variational hemivaritional inequalities abstract the existence of solutions to an elliptic hemivariational inequality involving the p laplacian is first established the variational hemivariational case which includes the above one is then examined when p 2 both of them are chiefly treated through mountain pass like critical point results for non differentiable functions

oscillatory retarded functional systems this note is concerned with the oscillatory behavior of a linear retarded system several criteria are obtained for having the system oscillatory conditions regarding the existence of nonoscillatory solutions are also given

generalized variational and quasi variational inequalities with discontinuous operators abstract we study the existence of solutions to generalized variational and generalized quasi variational inequalities with discontinuous operators we obtain results which generalize and extend previously known theorems we also compare our new continuity condition on the operator in the variational inequality to previously used continuity conditions we then apply our results to generalized variational inequalities which involve pseudo monotone operators

regularity and rothe method error estimates for parabolic hemivariational inequality this paper deals with regularity of solutions to the abstract operator version of parabolic partial differential inclusion of the form u t au t j u t f t with the multivalued term given in the form of clarke subdifferential of a locally lipschitz functional j using the rothe method it is shown that under appropriate assumptions on the data the solution has the increased regularity three regularity theorems are given the first one concerns the regularity of solution in the besov space b2 1 2 0 t h the second theorem provides assumption under which the solution lies in the space h1 0 t h l 0 t v c 0 t vweak the last one shows that if the operator a is strongly monotone and the multivalued term satisfies the relaxed monotonicity assumption then the unique solution also belongs to h1 0 t v w1 0 t h in the last case the error estimates on the rothe method are also proved

principal frequency and existence of solutions for quasilinear elliptic obstacle problems in this paper we are interested in the first eigenvalue of p laplacian and the relation between the first eigenvalue and the existence or nonexistence of nontrivial positive solution for quasilinear elliptic obstacle problems utilizing the fact that obstacle problem have consanguineous relations with corresponding equation we get a simple approach to study the properties of solutions of obstacle problems such as existence and nonexistence regularity and stability etc in this paper we are mainly concerned with the existence and nonexistence

evolutionary variational hemivariational inequalities existence and comparison results we consider an evolutionary quasilinear hemivariational inequality under constraints represented by some closed and convex subset our main goal is to systematically develop the method of sub supersolution on the basis of which we then prove existence comparison compactness and extremality results the obtained results are applied to a general obstacle problem we improve the corresponding results in the recent monograph s carl v k le d motreanu nonsmooth variational problems and their inequalities comparison principles and applications springer monogr math springer new york 2007

scattering by a circular cylinder buried under a slightly rough surface the cylindrical wave approach an analytical numerical technique for the scattering problem of a plane wave by a cylinder buried under a rough surface based on the cylindrical wave approach is presented the rough deviations on the interface are dealt with by means of the small perturbation method reflection and transmission coefficients are evaluated in a first order approximation and fields are the sum of a zeroth order solution relevant to flat surface and first order perturbation fields associated to the surface roughnesses numerical results are obtained through an exact evaluation of the spectral integrals giving results both in near and far field regions for the case of an interface with sinusoidal profile the approach is validated through comparisons with the literature and results showing the effect of geometrical and physical parameters on the scattered field are reported

on the existence of solutions for nonlinear parabolic problems with nonmonotone discontinuities abstract in this paper we consider a nonlinear parabolic problem with a discontinuous nonmonotone nonlinearity we assume the existence of an upper solution and a lower solution such that using results from the theory of pseudomonotone operators and from the theory of multivalued analysis together with truncation and penalization techniques we show that there exists at least one solution x t z such that t z x t z t z a e on t z

generalized quasi variational like hemivariational inequalities abstract in this paper we introduce and study a new class of generalized quasi variational like hemivariational inequalities with multi valued pseudomonotone operators in banach spaces some new existence theorems of solutions for this class of generalized quasi variational like hemivariational inequalities are proved the results presented in this paper generalize and extend some known results

existence results for evolution hemivariational inequalities of second order abstract in this paper we consider evolution hemivariational inequalities of second order with a time dependent pseudomonotone operator and nonmonotone multivalued perturbations we present the existence of solutions for such inequality the proof profits from a result on the surjectivity of operators of pseudomonotone type we discuss some examples which indicate the practical importance of our theoretical findings

general existence theorems for unilateral problems in continuum mechanics the problem of minimizing a possibly non convex and non coercive functional is studied either necessary or sufficient conditions for the existence of solutions are given involving a generalized recession functional whose properties are discussed thoroughly the abstract results are applied to find existence of equilibrium configurations of a deformable body subject to a system of applied forces and partially constrained to lie inside a possibly unbounded region

sub supersolution method for quasilinear parabolic variational inequalities this paper is about a systematic attempt to apply the sub supersolution method to parabolic variational inequalities we define appropriate concepts of sub supersolutions and derive existence comparison and extremity results for such inequalities

necessary and sufficient condition for oscillation of a neutral differential system with several delays abstract in this paper we prove that a general neutral differential system with several delays has a nonoscillatory solution if and only if its characteristic equations has a real root

monte carlo simulation of electromagnetic scattering from two dimensional random rough surfaces the fast multipole method fast fourier transform fmm fft method is developed to compute the scattering of an electromagnetic wave from a two dimensional 2 d rough surface the resulting algorithm computes a matrix vector multiply in o n log n operations this algorithm is shown to be more efficient than another o n log n algorithm the multilevel fast multipole algorithm mlfma for surfaces of small height for surfaces with larger roughness the mlfma is found to be more efficient using the mlfma monte carlo simulations are carried out to compute the statistical properties of the electromagnetic scattering from 2 d random rough surfaces using a workstation for the rougher surface backscattering enhancement is clearly observable as a pronounced peak in the backscattering direction of the computed bistatic scattering coefficient for the smoother surface the monte carlo results compare well with the results of the approximate kirchhoff theory

sub supersolution method and extremal solutions for higher order quasi linear elliptic hemi variational inequalities abstract in the present paper we generalize the sub supersolution method for a class of higher order quasi linear elliptic hemi variational inequalities using the notion of sub and supersolution we prove the existence comparison compactness and extremality results for the higher order quasi linear elliptic hemi variational inequality under considerations

finite dimensional approximation for a class of elliptic obstacle problems in this paper we study the finite dimensional approximation for a class of elliptic obstacle problems involving unbounded domains by using the galerkin method the convergence of the approximation is deduced

extremal solutions of quasilinear parabolic inclusions with generalized clarke s gradient abstract in this paper we consider an initial boundary value problem for a parabolic inclusion whose multivalued nonlinearity is characterized by clarke s generalized gradient of some locally lipschitz function and whose elliptic operator may be a general quasilinear operator of leray lions type recently extremality results have been obtained in case that the governing multivalued term is of special structure such as multifunctions given by the usual subdifferential of convex functions or subgradients of so called dc functions the main goal of this paper is to prove the existence of extremal solutions within a sector of appropriately defined upper and lower solutions for quasilinear parabolic inclusions with general clarke s gradient the main tools used in the proof are abstract results on nonlinear evolution equations regularization comparison truncation and special test function techniques as well as tools from nonsmooth analysis

existence and comparison principles for general quasilinear variational hemivariational inequalities we consider quasilinear elliptic variational hemivariational inequalities involving convex lower semicontinuous and locally lipschitz functionals we provide a generalization of the fundamental notion of sub and supersolutions on the basis of which we then develop the sub supersolution method for variational hemivariational inequalities including existence comparison compactness and extremality results

eigenvalue problems for nonlinear elliptic equations with unilateral constraints abstract in this paper we study eigenvalue problems for hemivariational and variational inequalities driven by the p laplacian differential operator using topological methods based on multivalued versions of the leray schauder alternative principle and variational methods based on the nonsmooth critical point theory we prove existence and multiplicity results for the eigenvalue problems that we examine

existence of solutions for generalized vector quasi variational like inequalities without monotonicity in this paper we introduce and study four kinds of generalized vector quasi variational like inequalities without monotonicity or pseudomonotonicity in hausdorff topological vector spaces by means of fixed point theorem we obtain some existence theorems of solutions for four kinds of generalized vector quasi variational like inequalities

a transformation media based approach for efficient monte carlo analysis of scattering from rough surfaces with objects this paper presents a computational model that utilizes transformation based metamaterials to enhance the performance of numerical modeling methods for achieving the statistical characterization of two dimensional electromagnetic scattering from objects on or above one dimensional rough sea surfaces monte carlo simulation of the rough surface scattering problem by means of differential equation based finite methods such as finite element or finite difference methods usually places a heavy burden on computational resources because at each realization of the monte carlo technique a mesh must be generated anew for each surface realization the main purpose of the proposed approach in this paper is to create a single mesh without repeating mesh generation at each step by introducing a transformation medium above the rough surface in the computational domain of the finite methods material parameters of the medium are obtained by the coordinate transformation technique which is based on the form invariance property of maxwell s equations at each realization only the material parameters are modified with respect to the geometry of surface without changing the mesh in this manner a great reduction in cpu time is achieved the proposed technique is analyzed and validated via various finite element simulations

existence of antiperiodic solutions for hemivariational inequalities in this paper we consider the problem of existence of antiperiodic solutions for first order and second order hemivariational inequalities with a pseudomonotone operator we first give the surjectivity result and then prove a existence of antiperiodic solutions for hemivariational inequalities with the surjectivity result