Existence and multiplicity of periodic solutions of the second-order differential equations with jumping nonlinearities
The author studies the existence and multiplicity of periodic solutions to the following equation \[ \ddot u + au^+ - bu^- +g(u) = p(t). \] Under some conditions on \(g\), he proves that there is at least one harmonic solution and determines the multiplicity of subharmonics. The proof is based on the Poincaré- Birkhoff twist theorem and on estimates on the time map.
scientific article; zbMATH DE number 1885860