An existence result for singular Finsler double phase problems

TL;DR

This paper establishes the existence of solutions for a class of singular Finsler double phase problems on Minkowski spaces, utilizing variational methods and addressing critical growth conditions.

Contribution

It is the first work to analyze a Finsler double phase operator, even in the nonsingular case, expanding the scope of variational methods in Finsler geometry.

Findings

Proved existence of at least one nontrivial weak solution.

Developed variational framework for Finsler double phase problems.

Addressed problems with critical growth in Minkowski spaces.

Abstract

In this paper, we study a class of singular double phase problems defined on Minkowski spaces in terms of Finsler manifolds and with right-hand sides that allow a certain type of critical growth for such problems. Under very general assumptions and based on variational tools we prove the existence of at least one nontrivial weak solution for such a problem. This is the first work dealing with a Finsler double phase operator even in the nonsingular case.