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 (7)

• Ground and bound state solutions of semilinear time-harmonic Maxwell equations in a bounded domain
• Ground states of a system of nonlinear Schrödinger equations with periodic potentials
• Multiple solutions to a nonlinear curl-curl problem in ${\mathbb{R}}^3$
• Nonlinear Schrödinger equations with sum of periodic and vanishing potentials and sign-changing nonlinearities
• Solutions to a nonlinear Maxwell equation with two competing nonlinearities in ${\mathbb{R}}^3$
• Bifurcation into spectral gaps for a noncompact semilinear Schrödinger equation with nonconvex potential
• Bound states for the Schrödinger equation with mixed-type nonlinearites