We study the existence of positive solutions for a semi-linear elliptic equation involving both critical growth and singular nonlinearity. By applying the Nehari manifold and Lusternik-Schnirelmann category theory to an auxiliary problem, we prove the existence of multiple positive solutions.

中文翻译：

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包含奇异非线性的临界椭圆问题的正解

我们研究了同时包含临界增长和奇异非线性的半线性椭圆方程正解的存在性。通过将Nehari流形和Lusternik-Schnirelmann类别理论应用于一个辅助问题，我们证明了多重正解的存在。