On a class of semilinear elliptic equations with boundary conditions and potentials which change sign

M. Ouanan and A. Touzani

Abstract and Applied Analysis, 2005, vol. 2005, 1-10

Abstract:

We study the existence of nontrivial solutions for the problem Δ u = u , in a bounded smooth domain Ω ⊂ ℝ ℕ , with a semilinear boundary condition given by ∂ u / ∂ ν = λ u − W ( x ) g ( u ) , on the boundary of the domain, where W is a potential changing sign, g has a superlinear growth condition, and the parameter λ ∈ ] 0 , λ 1 ] ; λ 1 is the first eigenvalue of the Steklov problem. The proofs are based on the variational and min-max methods.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:919184

DOI: 10.1155/AAA.2005.95

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