A semilinear elliptic problem involving nonlinear boundary condition and sign-changing potential

Abstract

In this paper, we study the multiplicity of nontrivial nonnegative solutions for a semilinear elliptic equation involving nonlinear boundary condition and sign-changing potential. With the help of the Nehari manifold, we prove that the semilinear elliptic equation: -Δu + u = λƒ(x)|u|q-2u in Ω, ∂u/∂v = g(x)|u|p-2u on ∂Ω, has at least two nontrivial nonnegative solutions for λ is sufficiently small.