a critical p biharmonic system with negative exponents abstract in this paper we are devoted to the study of critical p biharmonic system with a parameter which involves strongly coupled critical nonlinearities and negative exponents we prove that there exists a positive constant such that the above problem admits at least two solutions if 0

a semismooth equation approach to the solution of nonlinear complementarity problems in this paper we present a new algorithm for the solution of nonlinear complementarity problems the algorithm is based on a semismooth equation reformulation of the complementarity problem we exploit the recent extension of newton s method to semismooth systems of equations and the fact that the natural merit function associated to the equation reformulation is continuously differentiable to develop an algorithm whose global and quadratic convergence properties can be established under very mild assumptions other interesting features of the new algorithm are an extreme simplicity along with a low computational burden per iteration we include numerical tests which show the viability of the approach

on the connectedness of solution sets in linear complementarity problems abstract we investigate conditions on a square matrix m for which every lcp m q with q arbitrary has a connected solution set we show that a matrix with this property is necessarily fully semimonotone using degree theory we show that the solution set of lcp m q corresponding to a p 0 matrix is connected if there is a bounded connected component in the solution set

on a new homotopy continuation trajectory for nonlinear complementarity problems most known continuation methods for p 0 complementarity problems require some restrictive assumptions such as the strictly feasible condition and the properness condition to guarantee the existence and the boundedness of certain homotopy continuation trajectory to relax such restrictions we propose a new homotopy formulation for the complementarity problem based on which a new homotopy continuation trajectory is generated for p 0 complementarity problems the most promising feature of this trajectory is the assurance of the existence and the boundedness of the trajectory under a condition that is strictly weaker than the standard ones used widely in the literature of continuation methods particularly the often assumed strictly feasible condition is not required here when applied to p complementarity problems the boundedness of the proposed trajectory turns out to be equivalent to the solvability of the problem and the entire trajectory converges to the unique least element solution provided that it exists moreover for monotone complementarity problems the whole trajectory always converges to a least 2 norm solution provided that the solution set of the problem is nonempty the results presented in this paper can serve as a theoretical basis for constructing a new path following algorithm for solving complementarity problems even for the situations where the solution set is unbounded

approximate controllability of fractional evolution systems with riemann liouville fractional derivatives in this paper we deal with the control systems governed by fractional evolution differential equations involving riemann liouville fractional derivatives in banach spaces our main purpose in this article is to establish suitable assumptions to guarantee the existence and uniqueness results of mild solutions under these conditions the approximate controllability of the associated fractional evolution systems involving riemann liouville fractional derivatives is formulated and proved

extensions of the mountain pass theorem on considere une fonctionnelle c 1 i x r ou x est un espace de banach reel et ou i satisfait la condition de compacite de palais smale on presente une serie de theoremes qui generalisent le theoreme du col

application of degree theory in stability of the complementarity problem in this paper we study the behavior of a solution of the complementarity problem when the problem is perturbed the basic result is that if the degree of a certain function is nonzero then the problem is stable we show that several well known conditions for the existence of a solution to the problem also imply stability of the problem we also show that in the nondegenerate case there are simple conditions that ensure stability

weak univalence and connectedness of inverse images of continuous functions a continuous function f with domain x and range f x in rn is weakly univalent if there is a sequence of continuous one to one functions on x converging to f uniformly on bounded subsets of x in this article we establish under certain conditions the connectedness of an inverse image f 1 q the univalence results of radulescu radulescu more rheinboldt and gale nikaido follow from our main result we also show that the solution set of a nonlinear complementarity problem corresponding to a continuous p0 function is connected if it contains a nonempty bounded clopen set in particular the problem will have a unique solution if it has a locally unique solution

anti periodic solutions to nonlinear evolution equations abstract we deal with anti periodic problems for nonlinear evolution equations with nonmonotone perturbations the main tools in our study are the maximal monotone property of the derivative operator with anti periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings

on the analysis of a recurrent neural network for solving nonlinear monotone variational inequality problems we investigate the qualitative properties of a recurrent neural network rnn for solving the general monotone variational inequality problems vips defined over a nonempty closed convex subset which are assumed to have a nonempty solution set but need not be symmetric the equilibrium equation of the rnn system simply coincides with the nonlinear projection equation of the vip to be solved we prove that the rnn system has a global and bounded solution trajectory starting at any given initial point in the above closed convex subset which is positive invariant for the rnn system for general monotone vips we show by an example that the trajectory of the rnn system can converge to a limit cycle rather than an equilibrium in the case that the monotone vips are not symmetric contrary to this for the strictly monotone vips it is shown that every solution trajectory of the rnn system starting from the above closed convex subset converges to the unique equilibrium which is also locally asymptotically stable in the sense of lyapunov no matter whether the vips are symmetric or nonsymmetric for the uniformly monotone vips the aforementioned solution trajectory of the rnn system converges to the unique equilibrium exponentially

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

integral boundary value problems for first order integro differential equations with impulsive integral conditions this paper is concerned with the integral boundary value problems for first order integro differential equations with impulsive integral conditions sufficient conditions are obtained for the existence of extremal solutions

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

applications of degree theory to linear complementarity problems in this paper we consider two applications of degree theory to linear complementarity problems in the first application we study the stability of an lcp at a solution point specifically we prove the stability of an lcp corresponding to a p0 matrix at an isolated solution using a recent degree formula due to stewart 1991 we strengthen a stability result of gowda and pang 1992 in the second application we use the same degree formula of stewart to describe the number of solutions of lcpm q when m is a negative almost n matrix this analysis leads to a lipschitzian characterization of the solution map i q solm q corresponding to a nondegenerate negative matrix

on solution stability of the linear complementarity problem in the paper 5 c d ha introduced the notion of stability of a linear complementarity problem at a solution point and established several sufficient conditions for stability to hold in the present paper we derive some new stability results which significantly improve ha s results included in these new results are i a complete characterization of the stability condition under a nonsingularity assumption and ii further characterizations of solution stability in the case of a linear complementarity problem with a fully semimonotone matrix

nonlinear boundary value problems of fractional functional integro differential equations in this paper we consider the existence of generalized solutions for fractional functional integro differential equations of mixed type with nonlinear boundary value conditions by establishing a new comparison theorem and applying the monotone iterative technique we show the existence of extremal generalized solutions

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

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

a boundary value problem for fourth order elastic beam equations multiplicity results for a fourth order nonlinear boundary value problem are presented the proof of the main result is based on the critical point theory

a mountain pass theorem 143 in other words the mountain separating 0 and e may even be assumed of zero altitude and the conclusion is still true moreover as we shall show if c a the critical point can be chosen with llx ll r it is interesting to ask whether this extension of the ambrosetti rabinowitz theorem remains true in the infinite dimensional case we prove here that if 1 is strengthened a little to the form 1 there exist real numbers u r r such that 0 a for every x e a x e x y a moreover if c a the critical point can be chosen with r i x0 i r roughly speaking in brief the mountain pass theorem continues to hold for a mountain of zero altitude provided it also has non zero thickness in addition if c a the pass itself occurs precisely on the mountain i e satisfying r llroll r there are two interesting and immediate corollaries the first one says that a c function which has iwo local minimum points also has a third critical point the second states that a u periodic c function with a local minimum e has a critical point x e ku k 0 1 2 the precise statements of the above results will be given in the next sec tions the proof depends upon a lemma of clark 3 formulated here in a version suitable to our purpose in section 3 some applications are presen ted for the forced pendulum equation 2

structural and stability properties of p 0 nonlinear complementarity problems we consider p0 nonlinear complementarity problems and study the connectedness and stability of the solutions by applying degree theory and the mountain pass theorem to a smooth reformulation of the complementarity problem we show that the solution set is connected and bounded if a bounded isolated component of the solution set exists and that a solution is locally unique if and only if it is globally unique furthermore we prove that a solution is stable in ha s sense if and only if it is globally unique while the complementarity problem is stable if and only if the solution set is bounded

the structure of the critical set in the mountain pass theorem we show that the critical set generated by the mountain pass theorem of ambrosetti and rabinowitz must have a well defined structure in particular if the underlying banach space is infinite dimensional then either the critical set contains a saddle point of mountain pass type or the set of local minima intersects at least two components of the set of saddle points related conclusions are also established for the finite dimensional case and when other special conditions are assumed throughout the paper no hypotheses of nondegeneracy are required on the critical set

pc matrices and the linear complementarity problem abstract we introduce a new matrix class pc which consists of those matrices m for which the solution set of the corresponding linear complementarity problem is connected for every q rn we consider lemke s pivotal method from the perspective of piecewise linear homotopies and normal maps and show that lemke s method processes all matrices in pc q0 we further investigate the relationship of the class pc to other known matrix classes and show that column sufficient matrices are a subclass of pc as are 2 2 p0 matrices

existence of a solution for the fractional differential equation with nonlinear boundary conditions using the method of upper and lower solutions and its associated monotone iterative we present an existence theorem for a nonlinear fractional differential equation with nonlinear boundary conditions

stability of the linear complementarity problem at a solution point in this paper we study the behavior of a solution of the linear complementarity problem when data are perturbed we give characterizations of strong stability of the linear complementarity problem at a solution in the case of stability we give sufficient and necessary conditions

stability analysis of variational inequalities and nonlinear complementarity problems via the mixed linear complementarity problem and degree theory this paper is concerned with the mixed linear complementarity problem and the role it and its variants play in the stability analysis of the nonlinear complementarity problem and the karush kuhn tucker system of a variational inequality problem under a nonsingular assumption the mixed linear complementarity problem can be converted to the standard problem in this case the rich theory of the latter can be directly applied to the former in this work we employ degree theory to derive some sufficient conditions for the existence of a solution to the mixed linear complementarity problem in the absence of the nonsingularity property next we extend this existence theory to the mixed nonlinear complementarity problem and establish a main stability result under a certain degree theoretic assumption concerning the linearized problem we then specialize this stability result and its consequences to the parametric variational inequality problem under the assumption of a unique set of multipliers finally we

robustness and nondegenerateness for linear complementarity problems in this paper the main focus is on a stability concept for solutions of a linear complementarity problem a solution of such a problem is robust if it is stable against slight perturbations of the data of the problem relations are investigated between the robustness the nondegenerateness and the isolatedness of solutions it turns out that an isolated nondegenerate solution is robust and also that a robust nondegenerate solution is isolated since the class of linear complementarity problems with only robust solutions or only nondegenerate solutions is not an open set attention is paid to garcia s classgn of linear complementarity problems the nondegenerate problems ingn form an open set

anti periodic fractional boundary value problems we study a class of anti periodic boundary value problems of fractional differential equations some existence and uniqueness results are obtained by applying some standard fixed point principles several examples are given to illustrate the results

locating the least 2 norm solution of linear programs via a path following method a linear program has a unique least 2 norm solution provided that the linear program has a solution to locate this solution most of the existing methods were devised to solve certain equivalent perturbed quadratic programs or unconstrained minimization problems we provide in this paper a new theory which is different from these traditional methods and is an effective numerical method for seeking the least 2 norm solution of a linear program the essence of this method is a interior point like path following algorithm that traces a newly introduced regularized central path that is fairly different from the central path used in interior point methods one distinguishing feature of our method is that it imposes no assumption on the problem the iterates generated by this algorithm converge to the least 2 norm solution whenever the linear program is solvable otherwise the iterates converge to a point which gives a minimal kkt residual when the linear program is unsolvable

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

monotonicity of fixed point and normal mappings associated with variational inequality and its application we prove sufficient conditions for the monotonicity and the strong monotonicity of fixed point and normal maps associated with variational inequality problems over a general closed convex set sufficient conditions for the strong monotonicity of their perturbed versions are also shown these results include some well known in the literature as particular instances inspired by these results we propose a modified solodov and svaiter iterative algorithm for the variational inequality problem whose fixed point map or normal map is monotone

infinitely many sign changing solutions for a class of biharmonic equation without symmetry abstract in this paper via a perturbation theory we prove the existence of infinitely many sign changing solutions for a class of biharmonic equations

on the boundedness and stability of solutions to the affine variational inequality problem this paper investigates the boundedness and stability of solutions to the affine variational inequality problem the concept of a solution ray to a variational inequality defined by an affine mapping and on a closed convex set is introduced and characterized the connection of such a ray with the boundedness of the solution set of the given problem is explained in the case of the monotone affine variational inequality a complete description of the solution set is obtained which leads to a simplified characterization of the boundedness of this set as well as to a new error bound result for approximate solutions to such a variational problem the boundedness results are then combined with certain degree theoretic arguments to establish the stability of the solution set of an affine variational inequality problem