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| Notes on Homoclinic Solutions of the Steady Swift-Hohenberg Equation |
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Citation： |
Shengfu DENG,Boling GUO,Xiaopei LI.Notes on Homoclinic Solutions of the Steady Swift-Hohenberg Equation[J].Chinese Annals of Mathematics B,2013,34(6):917~920 |
| Page view： 1688
Net amount： 1240 |
Authors： |
Shengfu DENG; Boling GUO; Xiaopei LI; |
Foundation： |
PhD Start-up Fund of the Natural Science Foundation of GuangdongProvince (No. S2011040000464), the Project of Department of Education of Guangdong Province(No. 2012KJCX0074), the China Postdoctoral Science Foundation-Special Project (No. 201104077), theScientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry(No. (2012)940), the Natural Fund of Zhanjiang Normal University (No. LZL1101) and the DoctoralProject of Zhanjiang Normal University (No. ZL1109). |
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| Abstract： |
This paper considers the steady Swift-Hohenberg equation
u
+ β2u
+ u3 ? u = 0.
Using the dynamic approach, the authors prove that it has a homoclinic solution for each
β ∈ [ 4
√
8? 0, 4
√
8), where 0 is a small positive constant. This slightly complements Santra
and Wei’s result [Santra, S. and Wei, J., Homoclinic solutions for fourth order traveling
wave equations, SIAM J. Math. Anal., 41, 2009, 2038–2056], which stated that it admits
a homoclinic solution for each β ∈ (0, β0) where β0 = 0.9342 . |
Keywords： |
Homoclinic solutions, Normal form, Reversibility |
Classification： |
34B60, 34C37, 35B32, 37C29 |
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