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

M. Ouanan, A. Touzani
2005 Abstract and Applied Analysis  
We study the existence of nontrivial solutions for the problemΔu=u, in a bounded smooth domainΩ⊂ℝℕ, with a semilinear boundary condition given by∂u/∂ν=λu−W(x)g(u), on the boundary of the domain, whereWis a potential changing sign,ghas a superlinear growth condition, and the parameterλ∈]0,λ1];λ1is the first eigenvalue of the Steklov problem. The proofs are based on the variational and min-max methods.
doi:10.1155/aaa.2005.95 fatcat:igy4bld2wfclpjwcezgzuxygii