Multiple Solutions for Doubly Resonant Elliptic Problems Using Critical Groups

  • Ravi P. Agarwal Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901-6975, FL, U.S.A.
  • Michael E. Filippakis Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece.
  • Donal O’Regan Department of Mathematics, National University of Ireland, Galway, Ireland.
  • Nikolaos S. Papageorgiou Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece.
Keywords: Double resonance, C-condition, critical groups, critical point of mountain pass-type, Poincare-Hopf formula

Abstract

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.

Published
2008-10-01
How to Cite
[1]
R. P. Agarwal, M. E. Filippakis, D. O’Regan, and N. S. Papageorgiou, “Multiple Solutions for Doubly Resonant Elliptic Problems Using Critical Groups”, CUBO, vol. 10, no. 3, pp. 21–41, Oct. 2008.