We consider a semilinear elliptic equation, with a right hand side nonlinearity which may grow linearly. Throughout we assume a double resonance at infinity in the spectral interval [λ1, λ2]. In this paper, we can also have resonance at zero or even double resonance in the order interval [λm, λm+1], m ≥ 2. Using Morse theory and in particular critical groups, we prove two multiplicity theorems.
@article{1497,
title = {Multiple Solutions for Doubly Resonant Elliptic Problems Using Critical Groups},
journal = {CUBO, A Mathematical Journal},
volume = {10},
year = {2008},
language = {en},
url = {http://dml.mathdoc.fr/item/1497}
}
Agarwal, Ravi P.; Filippakis, Michael E.; O’Regan, Donal; Papageorgiou, Nikolaos S. Multiple Solutions for Doubly Resonant Elliptic Problems Using Critical Groups. CUBO, A Mathematical Journal, Tome 10 (2008) . http://gdmltest.u-ga.fr/item/1497/