Stationary waves of Schr\"{o}dinger-type equations with variable exponent

TL;DR

This paper investigates a class of nonlinear Schrödinger-type equations with variable exponents, establishing existence results through variational methods, contributing to the understanding of complex differential operators with non-constant growth conditions.

Contribution

It introduces new existence results for Schrödinger-type equations involving variable exponents using variational techniques, expanding the scope of nonlinear analysis.

Findings

Existence of solutions established for specific conditions.

Application of variational methods to variable exponent operators.

Advancement in understanding Schrödinger equations with non-standard growth.

Abstract

We are concerned with a class of nonlinear Schr\"{o}dinger-type equations with a reaction term and a differential operator that involves a variable exponent. By using related variational methods, we establish several existence results.