Abstract

This article focuses on the analysis of quasilinear equations influenced by the two-phase operator, commonly referred to as the ‘‘double-phase operator’’, while also incorporating a non-linear boundary condition. We prove the multiplicity of solutions through the utilization the method of Nehari manifold, complemented through the utilization of comparative techniques and critical point theory. Furthermore, determine the polarity of these solutions, distinctly identifying one as positive, another as negative, and a third as nodal.

中文翻译：

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结合非线性边界条件的两相罗宾问题

 抽象的

本文重点分析受两相算子（通常称为“双相算子”）影响的拟线性方程，同时还结合了非线性边界条件。我们通过利用 Nehari 流形方法证明了解的多重性，并通过比较技术和临界点理论的利用进行补充。此外，确定这些解决方案的极性，明确将一个解决方案标识为正极，另一个标识为负极，第三个标识为节点。