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

Yuhua Long; Yuhua Long

doi:10.3934/math.2021281

AIMS Mathematics

2021, Volume 6, Issue 5: 4786-4802. doi: 10.3934/math.2021281

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Research article

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

Yuhua Long ^{1,2
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1.
School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, PRC
2.
Center for Applied Mathematics, Guangzhou University, Guangzhou, 510006, PRC

Received: 25 November 2020 Accepted: 18 February 2021 Published: 25 February 2021
MSC : 39A12, 39A23

In the present paper, with the combination of a compactness lemma and variational techniques, we establish a sufficient condition to guarantee the existence of two nontrivial homoclinic solutions for a nonperiodic fourth-order difference equation with a perturbation. Our result generalizes and improves some known results.
- nonperiodic fourth-order difference equation,
- homoclinic solution,
- mountain pass theorem,
- variational technique
Citation: Yuhua Long. Existence of two homoclinic solutions for a nonperiodic difference equation with a perturbation[J]. AIMS Mathematics, 2021, 6(5): 4786-4802. doi: 10.3934/math.2021281

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Abstract

In the present paper, with the combination of a compactness lemma and variational techniques, we establish a sufficient condition to guarantee the existence of two nontrivial homoclinic solutions for a nonperiodic fourth-order difference equation with a perturbation. Our result generalizes and improves some known results.

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