Generalized linking-type theorem with applications to strongly indefinite problems with sign-changing nonlinearities

Abstract

We show the linking-type result which allows us to study strongly indefinite problems with sign-changing nonlinearities. We apply the abstract theory to the singular Schrödinger equation $$-\Delta u+V(x)u+\frac{a}{r^2}u=f(u)-\lambda g(u),x=(y,z)\in {\mathbb{R}}^K\times {\mathbb{R}}^{N-K},r=|y|,$$ where $$0\notin \sigma \left(-\Delta +\frac{a}{r^2}+V(x)\right).$$ As a consequence we obtain also the existence of solutions to the nonlinear curl-curl problem.

References in corpus (1)

• Bifurcation into spectral gaps for a noncompact semilinear Schrödinger equation with nonconvex potential