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Existence of Solution for a Class of Indefinite Variational Problems with Discontinuous Nonlinearity by Alves, Claudianor O.; Patricio, Geovany F. is a scholarly article available to read on EtoBox.

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This paper concerns the existence of a nontrivial solution for the following problem \begin{equation} \left\{\begin{aligned} -\Delta u + V(x)u & \in \partial_u F(x,u)\;\;\mbox{a.e. in}\;\;\mathbb{R}^{N},\nonumber u \in H^{1}(\mathbb{R}^{N}). \end{aligned} \right.\leqno{(P)} \end{equation} where $F(x,t)=\int_{0}^{t}f(x,s)\,ds$, $f$ is a $\mathbb{Z}^{N}$-periodic Caratheodory function and $\lambda=0$ does not belong to the spectrum of $-\Delta+V$. Here, $\partial_t F$ denotes the generalized gradient of $F$ with respect to variable $t$.

Author

Alves, Claudianor O.; Patricio, Geovany F.

Published

2020

Language

EN