Singular Finsler double phase problems with nonlinear boundary condition

TL;DR

This paper investigates a complex singular Finsler double phase problem with nonlinear boundary conditions and critical growth perturbations, proving the existence of solutions using variational and truncation methods, even in Euclidean cases.

Contribution

It is the first study to address a singular double phase problem with nonlinear boundary conditions in the Finsler setting.

Findings

Proved existence of at least one weak solution.

Developed variational and truncation techniques for such problems.

Extended results to Euclidean norm cases.

Abstract

In this paper we study a singular Finsler double phase problem with a nonlinear boundary condition and perturbations that have a type of critical growth, even on the boundary. Based on variational methods in combination with truncation techniques we prove the existence of at least one weak solution for this problem under very general assumptions. Even in the case when the Finsler manifold reduces to the Euclidean norm, our work is the first one dealing with a singular double phase problem and nonlinear boundary condition.