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Oliva, Francescantonio
Journal of mathematical analysis and applications, 04/2019, Letnik: 472, Številka: 1Journal Article
We prove existence of solutions to problems whose model is{−Δpu+uq=fuγinΩ,u≥0inΩ,u=0on∂Ω, where Ω is an open bounded subset of RN (N≥2), Δpu is the p-laplacian operator for 1≤p<N, q>0, γ≥0 and f is a nonnegative function in Lm(Ω) for some m≥1. In particular we analyze the regularizing effect produced by the absorption term in order to infer the existence of finite energy solutions in case γ≤1. We also study uniqueness of these solutions as well as examples which show the optimality of the results. Finally, we find local W1,p-solutions in case γ>1.
