Open AccessNonautonomous resonant periodic systems with indefinite linear part and a nonsmooth potential
Author(s) -
Dumitru Motreanu,
V. V. Motreanu,
Nikolaos S. Papageorgiou
Publication year - 2011
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2011.10.1401
Subject(s) - eigenvalues and eigenvectors , mathematics , infinity , linear system , reduction (mathematics) , mathematical analysis , periodic system , order (exchange) , pure mathematics , zero (linguistics) , physics , quantum mechanics , linguistics , philosophy , geometry , finance , economics
A nonautonomous second order system with a nonsmooth poten-tial 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 ei- genvalue. Also, it is assumed that the linearization of the system is indefinite. Using a nonsmooth variant of the reduction method and the local linking the- orem, we show that the system has at least two nontrivial solutions