A note on positive evanescent solutions for a certain class of elliptic problems |
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Authors: | Smaï l Djebali |
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Affiliation: | a Laboratory of EDP & HM, Department of Mathematics, E.N.S., P.O. Box 92, 16050 Kouba, Algiers, Algeria b Faculty of Mathematics and Computer Science, University of Lodz, S. Banacha 22, 90-238 Lodz, Poland |
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Abstract: | This paper is devoted to the existence and properties of solutions of the following class of nonlinear elliptic differential equations Δu(x)+f(x,u(x))+g(‖x‖)x⋅∇u(x)=0, x∈Rn, ‖x‖>R. We prove existence of positive solutions vanishing at positive infinity. Our approach is based on the subsolution and supersolution method. The nonlinearity f covers both sublinear and superlinear cases and does not necessarily satisfy f(x,0)≡0. The asymptotic behavior of solutions is also described. |
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Keywords: | Positive evanescent solutions Nonlinear elliptic equation Subsolution and supersolution method Asymptotic behavior |
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