Connectedness and compactness of weak efficient solutions for set-valued vector equilibrium problems.
We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.
The -convex functions are the viscosity subsolutions to the fully nonlinear elliptic equations , where is the elementary symmetric function of order , , of the eigenvalues of the Hessian matrix . For example, is the Laplacian and is the real Monge-Ampère operator det , while -convex functions and -convex functions are subharmonic and convex in the classical sense, respectively. In this paper, we establish an approximation theorem for negative -convex functions, and give several...
A bifurcation problem for variational inequalities is studied, where is a closed convex cone in , , is a matrix, is a small perturbation, a real parameter. The main goal of the paper is to simplify the assumptions of the abstract results concerning the existence of a bifurcation of periodic solutions developed in the previous paper and to give examples in more than three dimensional case.