MULTIPLE SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS WITH AN ASYMMETRIC REACTION TERM

作者：Kyritsi Sophia Th^*; Papageorgiou Nikolaos S

来源：Discrete and Continuous Dynamical Systems, 2013, 33(6): 2469-2494.

DOI：10.3934/dcds.2013.33.2469

• Nonlinear maximum principle
• superlinear reaction
• critical groups
• strong deformation retract
• homotopy invariance
• radial retraction

We consider a nonlinear Dirichlet problem driven by the p-Laplace differential operator. We assume that the Caratheodory reaction term f(z, x) exhibits an asymmetric behavior on the two semiaxes of IR. Namely, f(z, .) is (p - 1)-linear near -infinity and (p - 1)-superlinear near +infinity, but without satisfying the well-known Ambrosetti{Rabinowitz condition (AR-condition). Combining variational methods based on critical point theory, with suitable truncation techniques and Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign (one positive, the other negative).

• 出版日期2013-6
• 单位中国人民解放军海军大连舰艇学院