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
Asymptotically linear cooperative elliptic system: existence and multiplicity / Pomponio, A.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 52:3(2002), pp. 989-1003. [10.1016/S0362-546X(02)00148-7]
Asymptotically linear cooperative elliptic system: existence and multiplicity
Pomponio, A.
2002-01-01
Abstract
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 infinityI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.