Lane-Emden-Fowler equations with convection and singular potential |
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Authors: | Louis Dupaigne |
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Institution: | a LAMFA, Faculté de Mathématiques et d'Informatique, Université de Picardie Jules Verne, 33 rue Saint-Leu, 80039 Amiens, France b Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, RO-014700, Bucharest, Romania c Department of Mathematics, University of Craiova, 200585 Craiova, Romania |
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Abstract: | We are concerned with singular elliptic problems of the form −Δu±p(d(x))g(u)=λf(x,u)+μa|∇u| in Ω, where Ω is a smooth bounded domain in RN, d(x)=dist(x,∂Ω), λ>0, μ∈R, 0<a?2, and f is a nondecreasing function. We assume that p(d(x)) is a positive weight with possible singular behavior on the boundary of Ω and that the nonlinearity g is unbounded around the origin. Taking into account the competition between the anisotropic potential p(d(x)), the convection term a|∇u|, and the singular nonlinearity g, we establish various existence and nonexistence results. |
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Keywords: | 35B50 35J65 58J55 |
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