# Infinitely many solutions for a Schrodinger equation with sign-changing potential and nonlinear term

## TL;DR

This paper introduces a novel variational method to establish the existence of infinitely many solutions for a class of Schrödinger equations with sign-changing potentials and nonlinearities, broadening the scope of solvable indefinite problems.

## Contribution

It develops a new variational approach that does not require weak upper semicontinuity, enabling the discovery of multiple solutions for strongly indefinite Schrödinger equations with sign-changing nonlinear terms.

## Key findings

- Proves existence of infinitely many solutions
- Handles strongly indefinite linear parts
- Allows nonlinear terms to change sign

## Abstract

We propose a new variational approach to finding multiple critical points for strongly indefinite problems without assuming the weak upper semicontinuity on the variational functionals. By this approach, we obtain the existence of infinitely many geometrically distinct solutions for a stationary periodic Schr\"odinger equation, in which the linear part is strongly indefinite and the nonlinear term is allowed to change sign in general ways.