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On a singular nonlinear semilinear elliptic problem. (English) Zbl 0919.35044
The authors consider the singular boundary value problem \[ -\Delta u +K(x)u^{-\alpha} = \lambda u^p \quad\text{in } \Omega,\qquad u=0 \quad\text{ on } \partial \Omega \] where \(K(x) \in C^{2,\beta} (\overline{\Omega})\), \(\alpha, p \in (0,1)\) and \(\lambda\) is a real parameter. They study existence, uniqueness, regularity and the dependence on parameters of the positive solutions under various assumptions.

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35B65 Smoothness and regularity of solutions to PDEs
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