Pairs of solutions for Robin problems with an indefinite and unbounded potential, resonant at zero and infinity

摘要

We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential and a Caratheodory reaction term which is resonant both at zero and +/-infinity. Using the Lyapunov-Schmidt reduction method and critical groups (Morse theory), we show that the problem has at least two nontrivial smooth solutions.