Singular Finsler Double Phase Problems with Nonlinear Boundary Condition

In this paper, we study a singular Finsler double phase problem with a nonlinear boundary con-dition 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 bound-ary condition.

Automated summary

In this paper, the existence of at least one weak solution for a singular Finsler double phase problem with a nonlinear boundary condition and perturbations of critical growth is proven using variational methods combined with truncation techniques. This work is the first to address a singular double phase problem with a nonlinear boundary condition, even when the Finsler manifold reduces to the Euclidean norm.