非线性非齐次Robin问题的正解

Pub Date : 2015-10-29 DOI:10.4171/ZAA/1548

L. Gasiński, D. O’Regan, Nikolaos S. Papageorgiou

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引用次数: 10

摘要

考虑一类非线性非齐次Robin问题，该问题具有carathacimodory反应，满足在0+和+∞附近的某些一般增长条件。我们证明了正解的存在性和规律性，证明了最小正解的存在性，并在反应的附加条件下，证明了正解的唯一性。然后，我们证明了我们的设置包含某些感兴趣的参数罗宾方程，如非线性等扩散逻辑方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Positive Solutions for Nonlinear Nonhomogeneous Robin Problems

We consider a nonlinear, nonhomogeneous Robin problem with a Carathéodory reaction which satisfies certain general growth conditions near 0+ and near +∞. We show the existence and regularity of positive solutions, the existence of a smallest positive solution and under an additional condition on the reaction, we show the uniqueness of the positive solutions. We then show that our setting incorporates certain parametric Robin equations of interest such as nonlinear equidiffusive logistic equations.

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