Multiple Solutions for Noncoercive Problems with the p-Laplacian

作者：Gasinski Leszek^*; Papageorgiou Nikolaos S

来源：Bulletin of the Belgian Mathematical Society Simon Stevin, 2010, 17(1): 83-99.

We consider a nonlinear elliptic equation driven by the p-Laplacian and with a Caratheodory right hand side nonlinearity which exhibits an asymmetric asymptotic behaviour at +infinity and at -infinity These hypotheses imply that the Euler functional of the problem is noncoercive (indefinite) Using critical point theory, we prove the existence of at least two nontrivial smooth solutions Also in the last section for the asymmetric functionals considered here, we compute the critical groups at infinity

• 出版日期2010-3