Ambrosetti-Rabinowitz theorems revisited

preprint2013arXivOpen access

Abstract

We introduce tow assumptions weaker than the classical Ambrosetti-Rabinowitz and the subcritical polynomial growth conditions to obtain the Palais-Smale Condition. Therefore, we improve the Ambrosetti- Rabinowitz existence theorems. Also, we prove some existence results under a weaken subcritical polynomial growth conditions where the nonlinearity does not satisfy the super-quadratic condition and even it does not have any limits at infinity.

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