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Combined effects of singular and superlinear nonlinearities in some singular boundary value problems. (English) Zbl 1109.35344
Summary: This paper deals with a class of singular semilinear elliptic Dirichlet boundary value problems $$\cases \Delta u+\lambda u^{\beta}+p(x)u^{-\gamma}=0 \text{ in } \Omega,\\ u >0\text{ in }\Omega,\\ u =0 \text{ on } \partial\Omega, \endcases$$ where $\Omega$ is a bounded domain in $\Bbb R^{N}$ with smooth boundary $\partial\Omega$, $N\ge 3$, $p(x)$ is a nontrival nonnegative $L^2(\Omega)$ function, and $\beta,\gamma$ are constants satisfying $0<\gamma<1<\beta<2^*-1$ with $2^*:=2N/(N-2)$ where the combined effects of a superlinear and a singular term allow us to establish some existence and multiplicity results.

35J60Nonlinear elliptic equations
35J20Second order elliptic equations, variational methods
35J65Nonlinear boundary value problems for linear elliptic equations
Full Text: DOI
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