This work establishes existence of solution for resonant-superlinear elliptic problems using an appropriate Linking Theorem. The nonlinearity behaves as an asymptotic linear function at \(-\infty \) (resonant or not) and has a superlinear growth at \(+\infty \), with the eventual resonance phenomena occurring in a high order eigenvalue for the associated linear problem. Our main theorems are stated without the well-known Ambrosetti–Rabinowitz condition.

中文翻译：

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高阶特征值的共振超线性椭圆问题

这项工作使用适当的链接定理建立了共振超线性椭圆问题的解的存在性。非线性表现为\（-\ infty \）处的渐近线性函数（谐振或不谐振），并在\（+ \ infty \）处具有超线性增长，最终谐振现象以相关线性的高阶特征值发生问题。我们的主要定理是在没有众所周知的Ambrosetti–Rabinowitz条件的情况下陈述的。