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

We show a linking-type result which allows us to study strongly indefinite problems with sign- changing nonlinearities. We apply the abstract theory to the singular Schrodinger equation -Delta u + V(x)u + a/r(2)u = f(u) - lambda g(u), x = (y, z) is an element of R(K)xR(N-K), r = vertical bar y vertical bar, where 0 is not an element of sigma (-Delta + a/r(2) +V(x)). As a consequence we obtain also the existence of solutions to the nonlinear curl-curl problem.

Automated summary

We present a linking-type result that allows us to study strongly indefinite problems with sign-changing nonlinearities. We apply this abstract theory to the singular Schrodinger equation and also obtain the existence of solutions to the nonlinear curl-curl problem.