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Ground state homoclinic orbits of damped vibration problems

Guan-Wei Chen* and Jian Wang

Author Affiliations

School of Mathematics and Statistics, Anyang Normal University, Anyang, Henan, 455000, P.R. China

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Boundary Value Problems 2014, 2014:106  doi:10.1186/1687-2770-2014-106

Published: 9 May 2014


In this paper, we consider a class of non-periodic damped vibration problems with superquadratic nonlinearities. We study the existence of nontrivial ground state homoclinic orbits for this class of damped vibration problems under some conditions weaker than those previously assumed. To the best of our knowledge, there has been no work focused on this case.

MSC: 49J40, 70H05.

non-periodic damped vibration problems; ground state homoclinic orbits; superquadratic nonlinearity