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A note on existence of (anti-)periodic and heteroclinic solutions for a class of second-order odes

✍ Scribed by Kaizhi Wang; Yong Li

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 597 KB
Volume: 70
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2008.02.054

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✦ Synopsis

We discuss the existence of anti-periodic solutions to the following second-order differential equation q = u(t, q) by using fixed point theory together with the Green's function for the anti-periodic boundary value problem in the first part (Section 2) of the paper. Then in the next part (Section 3), we construct a kind of heteroclinic solution to some special cases of the equation above. Our method is variational in nature and is inspired by the ideas of Rabinowitz and Stredulinsky in [P. Rabinowitz, E. Stredulinsky, On some results of Moser and of Bangert, AIHP Anal. Nonlin. 21 (2004) 673-688].

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