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Infinitely many solutions for a class of fractional Hamiltonian systems via critical point theory
Author(s) -
Chen Peng,
He Xiaofei,
Tang X.H.
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3537
Subject(s) - mathematics , novelty , critical point (mathematics) , hamiltonian system , hamiltonian (control theory) , class (philosophy) , pure mathematics , mathematical physics , mathematical analysis , mathematical optimization , epistemology , philosophy , theology
In this paper, we are concerned with the existence of infinitely many solutions for the following fractional Hamiltonian systemstD ∞ α( − ∞D t α u ( t ) ) + L ( t ) u ( t ) = ∇ W ( t , u ( t ) ) ,u ∈ H α ( R , R n ) ,where α ∈ ( 1 / 2 , 1 ) , u ∈ R N , L ∈ C ( R , R N × N ) , and W ∈ C 1 ( R × R N , R ) . The novelty of this paper is that, relaxing the conditions on the potential function W ( t , x ), we obtain infinitely many solutions via critical point theory. Our results generalize and improve some existing results in the literature. Copyright © 2015 John Wiley & Sons, Ltd.