Existence and multiplicity of nonnegative solutions for semilinear elliptic problems involving nonlinearities indefinite in sign |
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Authors: | Giovanni Anello |
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Institution: | Department of Mathematics, University of Messina, Viale F. Stagno d’Alcontres 31, 98166 S.Agata, Messina, Italy |
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Abstract: | Let r,s∈]1,2 and λ,μ∈]0,+∞. In this paper, we deal with the existence and multiplicity of nonnegative and nonzero solutions of the Dirichlet problem with 0 boundary data for the semilinear elliptic equation −Δu=λus−1−ur−1 in Ω⊂RN, where N≥2. We prove that there exists a positive constant Λ such that the above problem has at least two solutions, at least one solution or no solution according to whether λ>Λ, λ=Λ or λ<Λ. In particular, a result by Hernandéz, Macebo and Vega is improved and, for the semilinear case, a result by Díaz and Hernandéz is partially extended to higher dimensions. Finally, an answer to a conjecture, recently stated by the author, is also given. |
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Keywords: | 35J20 35J25 |
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