Rocky Mountain Journal of Mathematics

Homoclinic orbits of nonlinear functional difference equations with Jacobi operators

Zhiguo Ren, Yuanbiao Zhang, Bo Zheng, and Haiping Shi

Full-text: Open access

Abstract

By using the critical point theory, the existence of a nontrivial homoclinic orbit which decays exponentially at infinity for difference equations containing both advance and retardation is obtained. The proof is based on the mountain pass lemma in combination with periodic approximations. Our results extend the results of 2007.

Article information

Source
Rocky Mountain J. Math., Volume 43, Number 6 (2013), 1991-2008.

Dates
First available in Project Euclid: 25 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1393336665

Digital Object Identifier
doi:10.1216/RMJ-2013-43-6-1991

Mathematical Reviews number (MathSciNet)
MR3178452

Zentralblatt MATH identifier
1302.37017

Subjects
Primary: 37C29: Homoclinic and heteroclinic orbits 37J45: Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods 39A10: Difference equations, additive 47J30: Variational methods [See also 58Exx]

Keywords
Homoclinic orbits subharmonics difference equations advance and retardation critical point theory

Citation

Ren, Zhiguo; Zhang, Yuanbiao; Zheng, Bo; Shi, Haiping. Homoclinic orbits of nonlinear functional difference equations with Jacobi operators. Rocky Mountain J. Math. 43 (2013), no. 6, 1991--2008. doi:10.1216/RMJ-2013-43-6-1991. https://projecteuclid.org/euclid.rmjm/1393336665


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