Multiple Solutions for Doubly Resonant Elliptic Problems Using Critical Groups
Agarwal, Ravi P.
Filippakis, Michael E.
Papageorgiou, Nikolaos S.
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.