The double-phase problem with a reaction term depending on the gradient is considered in this paper. Using the topological degree theory for a class of demicontinuous operators, we prove the existence of at least one solution of such problem. Our assumptions are suitable and different from those studied previously.

中文翻译：

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拓扑度双相问题解的存在性

本文考虑了反应项取决于梯度的双相问题。使用拓扑度理论对一类半连续算子，我们证明了该问题的至少一个解的存在。我们的假设是合适的，并且与先前研究的假设不同。