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 Schrödinger equation -Δu+V(x)u+ar2u=f(u)-λg(u),x=(y,z)∈RK×RN-K,r=|y|,where 0∉σ(-Δ+ar2+V(x)).As a consequence we obtain also the existence of solutions to the nonlinear curl-curl problem.
Bernini, F., Bieganowski, B. (2022). Generalized linking-type theorem with applications to strongly indefinite problems with sign-changing nonlinearities. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 61(5) [10.1007/s00526-022-02297-2].
Generalized linking-type theorem with applications to strongly indefinite problems with sign-changing nonlinearities
Bernini F.;
2022
Abstract
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 Schrödinger equation -Δu+V(x)u+ar2u=f(u)-λg(u),x=(y,z)∈RK×RN-K,r=|y|,where 0∉σ(-Δ+ar2+V(x)).As a consequence we obtain also the existence of solutions to the nonlinear curl-curl problem.
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