Existence and Concentration of Solutions for a Class of Elliptic Problems with Discontinuous Nonlinearity in $\mathbf{R}^{N}$

Abstract

Using variational methods we establish existence and concentration of positive solutions for a class of elliptic problems in $\mathbf{R}^{N}$, whose nonlinearity is discontinuous.

Existence of solution for a class of indefinite variational problems with discontinuous nonlinearity

“…A rich literature is available for problems with discontinuous nonlinearities, and we refer the reader to Chang [22], Ambrosetti and Badiale [12], Cerami [21], Alves et al [8], Alves et al [9], Alves and Bertone [10], Alves and Nascimento [11], Badiale [14], Dinu [25] and their references. Several techniques have been developed or applied in their study, such as variational methods for nondifferentiable functionals, lower and upper solutions, global branching, and the theory of multivalued mappings.…”

Existence of solution for Schrödinger equation with discontinuous nonlinearity and critical Growth

“…A rich literature is available for problems with discontinuous nonlinearities, and we refer the reader to Chang [19], Ambrosetti and Badiale [10], Alves and Patricio [2], Cerami [14], Alves et al [6], Alves et al [7], Alves and Bertone [8], Alves and Nascimento [9], Cerami [14,15], Badiale [13], Dinu [22], Gasiński and Papageorgiou [25], Kourogenis and Papageorgiou [27], Mironescu and Rȃdulescu [30], Rȃdulescu [33][34][35][36][37][38] and their references. Several techniques have been developed or applied in their study, such as variational methods for nondifferentiable functionals, lower and upper solutions, global branching, and the theory of multivalued mappings.…”

On a nonlocal multivalued problem in an Orlicz-Sobolev space via Krasnoselskii's genus

“…On the other hand, in this study, the nonlinearity f can be discontinuous. There is by now an extensive literature on multivalued equations and we refer the reader to [4], [20], [6], [5], [11], and references therein. The interest in the study of nonlinear partial differential equations with discontinuous nonlinearities has increased because many free boundary problems arising in mathematical physics may be stated in this form.…”