Fractional double phase Robin problem involving variable order-exponents and Logarithm-type nonlinearity

TL;DR

This paper investigates the existence of solutions for a new class of fractional Robin equations with variable exponents and logarithm-type nonlinearities, covering both critical and subcritical cases.

Contribution

It introduces a novel fractional Robin problem involving variable exponents and logarithmic nonlinearities, expanding the understanding of such equations.

Findings

Existence of solutions in critical and subcritical cases

Extension of fractional Robin problems with variable exponents

Handling of logarithm-type nonlinearities

Abstract

In this paper, we study the existence of solutions for the new fractinal Robin equations with variable exponents. Moreover, we deal with the logarithm-type nonlinearity. In particular, we consider two cases: critical and subcritical cases.