On generalized strong vector variational-like inequalities in Banach spaces.
We consider noncoercive functionals on a reflexive Banach space and establish minimization theorems for such functionals on smooth constraint manifolds. The functionals considered belong to a class which includes semi-coercive, compact-coercive and P-coercive functionals. Some applications to nonlinear partial differential equations are given.
The paper deals with the generalized Signorini problem. The used method of pseudomonotone semicoercive operator inequality is introduced in the paper by O. John. The existence result for smooth domains from the paper by O. John is extended to technically significant "angular" domains. The crucial point of the proof is the estimation of the nonlinear term which appears in the operator form of the problem. The substantial technical difficulties connected with non-smoothness of the boundary are overcome...
The purpose of this paper is to make a brief review of results obtained in the theory of variational inequalities for nonclassical operators, namely, of degenerate hyperbolic and variable type.
We consider a multi-polaron model obtained by coupling the many-body Schrödinger equation for N interacting electrons with the energy functional of a mean-field crystal with a localized defect, obtaining a highly non linear many-body problem. The physical picture is that the electrons constitute a charge defect in an otherwise perfect periodic crystal. A remarkable feature of such a system is the possibility to form a bound state of electrons via their interaction with the polarizable background....