Infinitely many homoclinic solutions for a class of damped vibration problems | Zendy

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Infinitely many homoclinic solutions for a class of damped vibration problems

Author(s) -

Chen Peng,

Tang X. H.

Publication year - 2014

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.2978

Subject(s) - homoclinic orbit , mathematics , class (philosophy) , vibration , mathematical analysis , calculus (dental) , nonlinear system , bifurcation , acoustics , physics , computer science , medicine , dentistry , quantum mechanics , artificial intelligence

In this paper, we deal with the existence of infinitely many homoclinic solutions for the damped vibration problems ü ( t ) + A u ̇ ( t ) − L ( t ) u ( t ) + ∇ W ( t , u ( t ) ) = 0 , where A is an antisymmetry N × N constant matrix, we establish some new existence results to guarantee that the above system has infinitely many homoclinic solutions under more relaxed assumptions on W ( t , x ), which satisfies a kind of new subquadratic condition by using fountain theorem. Recent results in the literature are generalized and significantly improved. Copyright © 2013 John Wiley & Sons, Ltd.

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