We consider a double phase Robin problem with a Carathéodory nonlinearity. When the reaction is superlinear but without satisfying the Ambrosetti–Rabinowitz condition, we prove an existence theorem. When the reaction is resonant, we prove a multiplicity theorem. Our approach is Morse theoretic, using the notion of homological local linking.

中文翻译：

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双阶段Robin问题解的存在性和多重性

我们考虑带有Carathéodory非线性的双相Robin问题。当反应超线性但不满足Ambrosetti-Rabinowitz条件时，我们证明了存在定理。当反应共振时，我们证明了一个多重定理。我们的方法是莫尔斯理论，使用了同源局部链接的概念。