Anti‐periodic solutions for a gradient system with resonance via a variational approach | Zendy

Tian Yu | Zendy; Henderson Johnny | Zendy

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Anti‐periodic solutions for a gradient system with resonance via a variational approach

Author(s) -

Tian Yu,

Henderson Johnny

Publication year - 2013

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201200110

Subject(s) - mathematics , eigenvalues and eigenvectors , action (physics) , boundary value problem , mathematical analysis , resonance (particle physics) , dual (grammatical number) , periodic boundary conditions , order (exchange) , boundary values , principle of least action , classical mechanics , physics , art , literature , particle physics , quantum mechanics , finance , economics

In this paper, we investigate a second‐order resonance anti‐periodic boundary value problemq ̈ ( t ) + λ m q ( t ) + ∇ F ( t , q ( t ) ) = 0 , t ∈ [ 0 , T ] ,q ( 0 ) = − q ( T ) ,q ̇ ( 0 ) = − q ̇ ( T ) ,where λ m is the m ‐th eigenvalue of the corresponding eigenvalue problem. By using the dual least action principle, we obtain an existence result. In addition, we obtain the existence of 2T‐periodic solutions forq ̈ ( t ) + λ m q ( t ) + ∇ F ( t , q ( t ) ) = 0 , t ∈ R .

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