MULTIPLICITY THEOREMS FOR RESONANT AND SUPERLINEAR NONHOMOGENEOUS ELLIPTIC EQUATIONS

作者：Papageorgiou Nikolaos S^*; Radulescu Vicentiu D

来源：Topological Methods in Nonlinear Analysis, 2016, 48(1): 283-320.

DOI：10.12775/TMNA.048

• Resonance
• multiple solution
• superlinear reaction
• nodal solutions
• critical groups

We consider nonlinear elliptic equations driven by the sum of a p-Laplacian (p > 2) and a Laplacian. We consider two distinct cases. In the first one, the reaction f (z, center dot) is (p-1)-linear near +/-infinity and resonant with respect to a nonprincipal variational eigenvalue of (-Delta p, W-0(1,p)(Omega)). We prove a multiplicity theorem producing three nontrivial solutions. In the second case, the reaction f (z, center dot) is (p - 1)-superlinear but does not satisfy the Ambrosetti-Rabinowitz condition. We prove two multiplicity theorems. In the first main result we produce six nontrivial solutions all with sign information and in the second theorem we have five nontrivial solutions. Our approach uses variational methods combined with the Morse theory, truncation methods, and comparison techniques.

• 出版日期2016-9