Sublinear singular elliptic problems with two parameters |
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Authors: | Marius Ghergu |
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Affiliation: | Department of Mathematics, University of Craiova, A.I. Cuza Street No. 13, 1100 Craiova, Romania |
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Abstract: | We establish several existence and nonexistence results for the boundary value problem −Δu+K(x)g(u)=λf(x,u)+μh(x) in Ω, u=0 on ∂Ω, where Ω is a smooth bounded domain in , λ and μ are positive parameters, h is a positive function, while f has a sublinear growth. The main feature of this paper is that the nonlinearity g is assumed to be unbounded around the origin. Our analysis shows the importance of the role played by the decay rate of g combined with the signs of the extremal values of the potential K(x) on . The proofs are based on various techniques related to the maximum principle for elliptic equations. |
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Keywords: | 35B50 35J65 58J55 |
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