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Existence and regularity to an elliptic equation with logarithmic nonlinearity
Authors:Marcelo Montenegro,Olivâ  ine Santana de Queiroz
Affiliation:Universidade Estadual de Campinas, IMECC, Departamento de Matemática, Caixa Postal 6065, CEP 13083-970, Campinas, SP, Brazil
Abstract:We study the nonlinear elliptic problem −Δu=χ{u>0}(logu+λf(x,u)) in ΩRn with u=0 on ∂Ω. The function View the MathML source is nondecreasing, sublinear and fu is continuous. For every λ>0, we obtain a maximal solution uλ?0 and prove its global regularity View the MathML source. There is a constant λ such that uλ vanishes on a set of positive measure for 0<λ<λ, and uλ>0 for λ>λ. If f is concave, for λ>λ we characterize uλ by its stability.
Keywords:35J65   35B20   35B35   35B65
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