Nontrivial solutions for Neumann problems with an indefinite linear part

作者：Gasinski Leszek^*; Papageorgiou Nikolaos S

来源：Applied Mathematics and Computation, 2010, 217(6): 2666-2675.

DOI：10.1016/j.amc.2010.08.004

• Indefinite linear part
• Ambrosetti-Rabinowitz condition
• Superlinear nonlinearity
• Cerami condition
• Local linking
• Spectral decomposition
• Neumann problem

In this paper, we consider a semilinear Neumann problem with an indefinite linear part and a Caratheodory nonlinearity which is superlinear near infinity and near zero, but does not satisfy the Ambrosetti-Rabinowitz condition. Using an abstract existence theorem for C(1)-functions having a local linking at the origin, we establish the existence of at least one nontrivial smooth solution.

• 出版日期2010-11-15