NONAUTONOMOUS RESONANT PERIODIC SYSTEMS WITH INDEFINITE LINEAR PART AND A NONSMOOTH POTENTIAL

作者：Motreanu D^*; Motreanu V V; Papageorgiou N S

来源：Communications on Pure and Applied Analysis, 2011, 10(5): 1401-1414.

DOI：10.3934/cpaa.2011.10.1401

• Resonant system
• indefinite linear part
• reduction method
• coercive functional
• local linking
• C-condition

A nonautonomous second order system with a nonsmooth potential is studied. It is assumed that the system is asymptotically linear at infinity and resonant (both at infinity and at the origin), with respect to the zero eigenvalue. Also, it is assumed that the linearization of the system is indefinite. Using a nonsmooth variant of the reduction method and the local linking theorem, we show that the system has at least two nontrivial solutions.

• 出版日期2011-9