Asymptotically linear cooperative elliptic system: existence and multiplicity

In this paper we consider an asymptotically linear cooperative elliptic system at resonance. By a penalization technique and by the use of Morse theory, we prove, firstly, the existence of a non-zero solution if the difference between the Morse index at zero and the Morse index at infinity is big enough. Later on we will prove the existence of N - 1 pairs of non-trivial solutions, where N is, roughly speaking, the difference between the Morse index at zero and the Morse index at infinity