Existence and nonexistence results for classes of singular elliptic problem. (English) Zbl 1207.35168

Zhang, Peng; Liao, Jia-Feng

Abstr. Appl. Anal. 2010, Article ID 435083, 10 p. (2010).

Summary: The singular semilinear elliptic problem \(-\Delta u+k(x)u^{-\gamma}= \lambda u^p\) in \(\Omega\), \(u>0\) in \(\Omega\), \(u=0\) on \(\partial\Omega\), is considered, where \(\Omega\) is a bounded domain with smooth boundary in \(\mathbb R^N\), \(k\in C_{\text{loc}}^a(\Omega)\cap C(\overline{\Omega})\), and \(\gamma,p,\lambda\) are three positive constants. Some existence or nonexistence results are obtained for solutions of this problem by the sub-supersolution method.

MSC:

35J75	Singular elliptic equations
35J61	Semilinear elliptic equations
35J20	Variational methods for second-order elliptic equations

Keywords:

singular semilinear ellipitc problem; existence; sub-supersolution method

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