Resonant noncooperative elliptic systems via relative morse indices and linking method

We consider an asymptotically linear noncooperative elliptic system with possibly more than one resonant level. For this purpose, the relative Morse index in Abbondandolo (Morse theory for Hamiltonian systems, 2001), and a Morse theory developed in Hirano et al. (Calc Var Partial Differ Equ 10:223–247, 2000) are combined. As a complement, we also provide a result based on the linking method. Due to the abstract nature of the framework, some examples are also given.