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.

中文翻译：

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奇异Finsler双相问题的存在性结果

在本文中，我们研究了在Finkler流形和Minkowski空间上定义的一类奇异双相问题，该问题的右手侧允许这类问题的某种临界增长。在非常笼统的假设下，基于变分工具，我们证明了至少一个针对此类问题的非平凡弱解的存在。即使在非奇异情况下，这也是处理Finsler双相算子的第一项工作。