Fractional double phase Robin problem involving variable order-exponents without Ambrosetti-Rabinowitz condition

TL;DR

This paper studies a fractional double phase Robin problem with variable order and exponents, using variational methods to establish multiple solutions without relying on the Ambrosetti-Rabinowitz condition.

Contribution

It introduces a novel analysis of a fractional double phase problem with variable exponents, avoiding the traditional Ambrosetti-Rabinowitz condition.

Findings

Established existence of multiple solutions

Applied variational methods to a complex fractional problem

Extended analysis to variable order and exponents

Abstract

We consider a fractional double phase Robin problem involving variable order and variable exponents. The nonlinearity $f$ is a Carath\'{e}odory function satisfying some hypotheses which do not include the Ambrosetti-Rabinowitz type condition. By using Variational methods, we investigate the multiplicity of solutions.