Open Access
2013 Homoclinic orbits of nonlinear functional difference equations with Jacobi operators
Zhiguo Ren, Yuanbiao Zhang, Bo Zheng, Haiping Shi
Rocky Mountain J. Math. 43(6): 1991-2008 (2013). DOI: 10.1216/RMJ-2013-43-6-1991


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.


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Zhiguo Ren. Yuanbiao Zhang. Bo Zheng. Haiping Shi. "Homoclinic orbits of nonlinear functional difference equations with Jacobi operators." Rocky Mountain J. Math. 43 (6) 1991 - 2008, 2013.


Published: 2013
First available in Project Euclid: 25 February 2014

zbMATH: 1302.37017
MathSciNet: MR3178452
Digital Object Identifier: 10.1216/RMJ-2013-43-6-1991

Primary: 37C29 , 37J45 , 39A10 , 47J30

Keywords: advance and retardation , Critical point theory , difference equations , Homoclinic orbits , subharmonics

Rights: Copyright © 2013 Rocky Mountain Mathematics Consortium

Vol.43 • No. 6 • 2013
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