On a Class of Semilinear Elliptic Equations with Boundary Conditions and Potentials Which Change Sign
نویسنده
چکیده
We study the existence of nontrivial solutions for the problem ∆u = u, in a bounded smooth domain Ω ⊂ RN, with a semilinear boundary condition given by ∂u/∂ν = λu− 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,λ1]; λ1 is the first eigenvalue of the Steklov problem. The proofs are based on the variational and min-max methods.
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