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: $$displaylines{ -Delta u+u=lambda f(x)|u|^{q-2}u quad hbox{in }Omega , cr frac{partial u}{partial u }=g(x)|u| ^{p-2}u quad hbox{on }partial Omega , }$$has at least two nontrivial nonnegative solutions for $lambda $is sufficiently small.

Keywords

• Semilinear elliptic equations
• Nehari manifold
• Nonlinear boundary condition.