Homoclinic solutions of a class of periodic difference equations with asymptotically linear nonlinearities

2013 ◽  
Vol 89 ◽  
pp. 208-218 ◽  
Author(s):  
Juhong Kuang ◽  
Zhiming Guo
Keyword(s):  
Difference Equations ◽  
Homoclinic Solutions ◽  
Asymptotically Linear

scholarly journals Existence and Multiplicity Results of Homoclinic Solutions for the DNLS Equations with Unbounded Potentials

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Defang Ma ◽  
Zhan Zhou
Keyword(s):  
Difference Equations ◽  
Mountain Pass Theorem ◽  
Sufficient Conditions ◽  
Homoclinic Solutions ◽  
Fountain Theorem ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Special Cases ◽  
Discrete Nonlinear Schrödinger Equations ◽  
The Difference

A class of difference equations which include discrete nonlinear Schrödinger equations as special cases are considered. New sufficient conditions of the existence and multiplicity results of homoclinic solutions for the difference equations are obtained by making use of the mountain pass theorem and the fountain theorem, respectively. Recent results in the literature are generalized and greatly improved.

scholarly journals Homoclinic solutions of 2nth-order difference equations containing both advance and retardation

2016 ◽  
Vol 14 (1) ◽  
pp. 520-530 ◽  
Author(s):  
Yuhua Long ◽  
Yuanbiao Zhang ◽  
Haiping Shi
Keyword(s):  
Difference Equation ◽  
Critical Point ◽  
Difference Equations ◽  
Homoclinic Solutions ◽  
Mountain Pass ◽  
Nonlinear Difference Equation ◽  
Mountain Pass Lemma ◽  
Order Difference ◽  
Existence And Multiplicity ◽  
New Criteria

AbstractBy using the critical point method, some new criteria are obtained for the existence and multiplicity of homoclinic solutions to a 2nth-order nonlinear difference equation. The proof is based on the Mountain Pass Lemma in combination with periodic approximations. Our results extend and improve some known ones.

scholarly journals Nontrivial periodic solutions to delay difference equations via Morse theory

2018 ◽  
Vol 16 (1) ◽  
pp. 885-896 ◽  
Author(s):  
Yuhua Long ◽  
Haiping Shi ◽  
Xiaoqing Deng
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
Morse Theory ◽  
Sufficient Conditions ◽  
Asymptotically Linear ◽  
Linear Delay ◽  
Nontrivial Periodic Solutions ◽  
Delay Difference Equations ◽  
Delay Difference

AbstractIn this paper some sufficient conditions are obtained to guarantee the existence of nontrivial 4T + 2 periodic solutions of asymptotically linear delay difference equations. The approach used is based on Morse theory.

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