A note on the existence results for Schrodinger-Maxwell system with super-criticalnonlinearitie

TL;DR

This paper extends the existence results for the Schrödinger-Maxwell system to supercritical nonlinearities using a new variational principle, building on known subcritical case results.

Contribution

It introduces a novel variational approach to establish solutions for supercritical nonlinearities in the Schrödinger-Maxwell system, which was previously known only for subcritical cases.

Findings

Existence of at least one non-trivial weak solution for supercritical nonlinearities.

Extension of known results from subcritical to supercritical cases.

Application of a new variational principle to the problem.

Abstract

The paper considers the Schrodinger-Maxwell system with supercritical nonlinearitie. We prove the existence of at least one non-trivial weak solution. This result is already known for the subcritical case. In this paper, we extend it to the supercritical values of p as well. We use a new variational principle to prove our result.