Abstract

Critical point results for a 2nth-order differential equation with Sturm-liouville operator is exploited in order to prove that a suitable class possesses at least one solution under an asymptotical behavior of the potential of the nonlinear term at zero, and also possesses infinitely many solutions under some hypotheses on the behavior of the potential of the nonlinear term at infinity. Some recent results are extended and improved. Some examples are included to dwell upon the usefulness of the results obtained.

中文翻译：

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具有 Sturm-Liouville 算子的二阶微分方程的存在性结果

摘要

利用具有 Sturm-liouville 算子的二阶微分方程的临界点结果，以证明合适的类在非线性项的势为零的渐近行为下至少具有一个解，并且还具有无限多个解在关于无穷远非线性项的势能行为的一些假设下。最近的一些结果得到了扩展和改进。包括一些例子来详细说明所获得结果的有用性。