# Robin problems with a general potential and a superlinear reaction

## TL;DR

This paper investigates semilinear Robin boundary value problems involving indefinite potentials and superlinear reactions without the Ambrosetti-Rabinowitz condition, establishing existence and multiplicity of solutions using advanced variational methods.

## Contribution

It introduces new existence and multiplicity results for Robin problems with indefinite potentials and superlinear reactions, without relying on the Ambrosetti-Rabinowitz condition.

## Key findings

- Proved existence of solutions using variational methods.
- Established multiplicity and infinity of solutions.
- Applied Morse theory and perturbation techniques.

## Abstract

We consider semilinear Robin problems driven by the negative Laplacian plus an indefinite potential and with a superlinear reaction term which need not satisfy the Ambrosetti-Rabinowitz condition. We prove existence and multiplicity theorems (producing also an infinity of smooth solutions) using variational tools, truncation and perturbation techniques and Morse theory (critical groups).