scholarly journals Existence of two homoclinic solutions for a nonperiodic difference equation with a perturbation

2021 ◽  
Vol 6 (5) ◽  
pp. 4786-4802
Author(s):  
Yuhua Long ◽  
◽  
Keyword(s):  
Difference Equation ◽  
Homoclinic Solutions

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 Weak homoclinic solutions of anisotropic difference equation with variable exponents

2012 ◽  
Vol 2012 (1) ◽  
pp. 154 ◽  
Author(s):  
Aboudramane Guiro ◽  
Blaise Kone ◽  
Stanislas Ouaro
Keyword(s):  
Difference Equation ◽  
Homoclinic Solutions ◽  
Variable Exponents

scholarly journals Sequences of positive homoclinic solutions to difference equations with variable exponent

2020 ◽  
Vol 70 (2) ◽  
pp. 417-430
Author(s):  
Robert Stegliński ◽  
Magdalena Nockowska-Rosiak
Keyword(s):  
Variational Principle ◽  
Difference Equation ◽  
Difference Equations ◽  
Critical Point Theory ◽  
Variable Exponent ◽  
Point Theory ◽  
Homoclinic Solutions ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation

Abstract We study the existence of infinitely many positive homoclinic solutions to a second-order difference equation on integers with pk-Laplacian. To achieve our goal we use the critical point theory and the general variational principle of Ricceri.

scholarly journals Homoclinic Solutions for a Higher Order ϕc-Laplacian Difference Equation Containing Both Advance and Retardation

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Peng Mei ◽  
Zhan Zhou
Keyword(s):  
Difference Equation ◽  
Critical Point ◽  
Critical Point Theory ◽  
Point Theory ◽  
Higher Order ◽  
Homoclinic Solutions ◽  
Nonlinear Difference Equation ◽  
Mixed Nonlinearities

We consider a 2mth-order nonlinear difference equation containing both advance and retardation with ϕc-Laplacian. Using the critical point theory, some new and concrete criteria for the existence of homoclinic solutions with mixed nonlinearities are obtained.

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