On a Convex Combination of Solutions to Elliptic Variational Inequalities
نویسندگان
چکیده
Let ugi the unique solutions of an elliptic variational inequality with second member gi (i = 1, 2). We establish necessary and sufficient conditions for the convex combination tug1 + (1 − t)ug2 , to be equal to the unique solution of the same elliptic variational inequality with second member tg1 + (1− t)g2. We also give some examples where this property is valid.
منابع مشابه
The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent
In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.
متن کاملExistence and Uniqueness Results for a Nonstandard Variational-Hemivariational Inequalities with Application
This paper aims at establishing the existence and uniqueness of solutions for a nonstandard variational-hemivariational inequality. The solutions of this inequality are discussed in a subset $K$ of a reflexive Banach space $X$. Firstly, we prove the existence of solutions in the case of bounded closed and convex subsets. Secondly, we also prove the case when $K$ is compact convex subsets. Fina...
متن کاملSub- Supersolutions and the Existence of Extremal Solutions in Noncoercive Variational Inequalities
The paper is concerned with the solvability of variational inequalities that contain second-order quasilinear elliptic operators and convex functionals. Appropriate concepts of suband supersolutions (for inequalities) are introduced and existence of solutions and extremal solutions are discussed.
متن کاملVariational inequalities on Hilbert $C^*$-modules
We introduce variational inequality problems on Hilbert $C^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. Then relation between variational inequalities, $C^*$-valued metric projection and fixed point theory on Hilbert $C^*$-modules is studied.
متن کاملExistence and multiplicity of nontrivial solutions for $p$-Laplacian system with nonlinearities of concave-convex type and sign-changing weight functions
This paper is concerned with the existence of multiple positive solutions for a quasilinear elliptic system involving concave-convex nonlinearities and sign-changing weight functions. With the help of the Nehari manifold and Palais-Smale condition, we prove that the system has at least two nontrivial positive solutions, when the pair of parameters $(lambda,mu)$ belongs to a c...
متن کامل