DOUBLE RESONANCE FOR ROBIN PROBLEMS WITH INDEFINITE AND UNBOUNDED POTENTIAL

作者：Papageorgiou Nikolaos S^*; Winkert Patrick

来源：Discrete and Continuous Dynamical Systems - Series S, 2018, 11(2): 323-344.

DOI：10.3934/dcdss.2018018

• Indefinite potential
• Robin boundary condition
• regularity theory
• critical groups
• multiple nontrivial solutions
• double resonance

We study a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential term. The nonlinearity f(x, s) is a Caratheodory function which is asymptotically linear as s -> +/-infinity and resonant. In fact we assume double resonance with respect to any nonprincipal, nonnegative spectral interval [(lambda) over cap (k), (lambda) over cap (k+1)]. Applying variational tools along with suitable truncation and perturbation techniques as well as Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of constant sign.

• 出版日期2018-4