Infinitely many homoclinic orbits for a class of second-order damped differential equations

We investigate the existence and multiplicity of homoclinic orbits for the second‐order damped differential equations For Equation 1 where L(t) and W(t,u) are neither autonomous nor periodic in t. Under certain assumptions on g, L, and W, we get infinitely many homoclinic orbits for superquadratic,...

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Published inMathematical methods in the applied sciences Vol. 38; no. 18; pp. 5048 - 5062
Main Authors Zhang, Chuanfang, Han, Zhiqing
Format Journal Article
LanguageEnglish
Published Freiburg Blackwell Publishing Ltd 01.12.2015
Wiley Subscription Services, Inc
Subjects
35A15
37J45
Autonomous
Copyrights
Critical point
damped differential equation
Differential equations
dual fountain theorem
fountain theorem
homoclinic orbit
Mathematical analysis
Nonlinearity
Orbits
subclass34C37
Theorems
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Summary:We investigate the existence and multiplicity of homoclinic orbits for the second‐order damped differential equations For Equation 1 where L(t) and W(t,u) are neither autonomous nor periodic in t. Under certain assumptions on g, L, and W, we get infinitely many homoclinic orbits for superquadratic, subquadratic and concave–convex nonlinearities cases by using fountain theorem and dual fountain theorem in critical point theory. These results generalize and improve some existing results in the literature. Copyright © 2015 JohnWiley & Sons, Ltd.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.3425