Nonautonomous resonant periodic systems with indefinite linear part and a nonsmooth potential | Zendy

Dumitru Motreanu | Zendy; V. V. Motreanu | Zendy; Νικόλαος Παπαγεωργίου | Zendy

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Nonautonomous resonant periodic systems with indefinite linear part and a nonsmooth potential

Author(s) -

Dumitru Motreanu,

V. V. Motreanu,

Νικόλαος Παπαγεωργίου

Publication year - 2011

Publication title -

communications on pure andamp 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

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