PAIRS OF NONTRIVIAL SOLUTIONS FOR RESONANT ROBIN PROBLEMS WITH INDEFINITE LINEAR PART

We study a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential and a Carath´eodory reaction term which exhibits linear growth near ±∞ and near zero. Resonance with respect to different eigenvalues can occur at both ±∞ and near zero. Using the saddle point reduction method and Morse theory (critical groups), we prove a multiplicity theorem producing two nontrivial smooth solutions.