An existence result for singular Finsler double phase problems

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 non-trivial weak solution for such a problem. This is the first work dealing with a Finsler double phase operator even in the nonsingular case. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper investigates a class of singular double phase problems on Minkowski spaces using Finsler manifolds, allowing certain critical growth for the right-hand sides. By employing variational tools under general assumptions, the existence of at least one non-trivial weak solution for such a problem is proven. This marks the first work dealing with a Finsler double phase operator, even in the nonsingular case.