HOMOCLINIC SOLUTIONS OF NONLINEAR LAPLACIAN DIFFERENCE EQUATIONS WITHOUT AMBROSETTI-RABINOWITZ CONDITION

doi:10.1007/s10473-021-0305-z

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (3): 712-718.doi: 10.1007/s10473-021-0305-z

HOMOCLINIC SOLUTIONS OF NONLINEAR LAPLACIAN DIFFERENCE EQUATIONS WITHOUT AMBROSETTI-RABINOWITZ CONDITION

Antonella NASTASI¹, Stepan TERSIAN², Calogero VETRO¹

1. University of Palermo, Department of Mathematics and Computer Science, Via Archirafi 34, 90123, Palermo, Italy;
2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria

收稿日期:2019-04-16 修回日期:2020-08-08 出版日期:2021-06-25 发布日期:2021-06-07
通讯作者: Calogero VETRO E-mail:calogero.vetro@unipa.it
作者简介:Antonella NASTASI,E-mail:antonella.nastasi@unipa.it;Stepan TERSIAN,E-mail:sterzian@uni-ruse.bg
基金资助:
The second author is supported by the Bulgarian National Science Fund under Project DN 12/4 “Advanced analytical and numerical methods for nonlinear differential equations with applications in finance and environmental pollution”, 2017.

HOMOCLINIC SOLUTIONS OF NONLINEAR LAPLACIAN DIFFERENCE EQUATIONS WITHOUT AMBROSETTI-RABINOWITZ CONDITION

Antonella NASTASI¹, Stepan TERSIAN², Calogero VETRO¹

1. University of Palermo, Department of Mathematics and Computer Science, Via Archirafi 34, 90123, Palermo, Italy;
2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria

Received:2019-04-16 Revised:2020-08-08 Online:2021-06-25 Published:2021-06-07
Contact: Calogero VETRO E-mail:calogero.vetro@unipa.it
About author:Antonella NASTASI,E-mail:antonella.nastasi@unipa.it;Stepan TERSIAN,E-mail:sterzian@uni-ruse.bg
Supported by:
The second author is supported by the Bulgarian National Science Fund under Project DN 12/4 “Advanced analytical and numerical methods for nonlinear differential equations with applications in finance and environmental pollution”, 2017.

摘要/Abstract

摘要： The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using Ambrosetti-Rabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.

关键词: Difference equations, homoclinic solutions, non-zero solutions, (p,q)-Laplacian operator

Abstract: The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using Ambrosetti-Rabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.

Key words: Difference equations, homoclinic solutions, non-zero solutions, (p,q)-Laplacian operator

中图分类号:

34B18

Antonella NASTASI, Stepan TERSIAN, Calogero VETRO. HOMOCLINIC SOLUTIONS OF NONLINEAR LAPLACIAN DIFFERENCE EQUATIONS WITHOUT AMBROSETTI-RABINOWITZ CONDITION[J]. 数学物理学报(英文版), 2021, 41(3): 712-718.

Antonella NASTASI, Stepan TERSIAN, Calogero VETRO. HOMOCLINIC SOLUTIONS OF NONLINEAR LAPLACIAN DIFFERENCE EQUATIONS WITHOUT AMBROSETTI-RABINOWITZ CONDITION[J]. Acta mathematica scientia,Series B, 2021, 41(3): 712-718.

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HOMOCLINIC SOLUTIONS OF NONLINEAR LAPLACIAN DIFFERENCE EQUATIONS WITHOUT AMBROSETTI-RABINOWITZ CONDITION

HOMOCLINIC SOLUTIONS OF NONLINEAR LAPLACIAN DIFFERENCE EQUATIONS WITHOUT AMBROSETTI-RABINOWITZ CONDITION

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