Existence and nonexistence of positive solutions to a class of nonlocal discrete Kirchhoff type equations

Yuhua Long; Yuhua Long

doi:10.3934/math.20231253

AIMS Mathematics

2023, Volume 8, Issue 10: 24568-24589. doi: 10.3934/math.20231253

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Existence and nonexistence of positive solutions to a class of nonlocal discrete Kirchhoff type equations

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

Received: 11 May 2023 Revised: 07 August 2023 Accepted: 15 August 2023 Published: 18 August 2023
MSC : 39A10, 34B15, 35B38

In this paper, we investigate the existence and nonexistence of positive solutions to a class of nonlocal partial difference equations via a variant version of the mountain pass theorem. The conditions in our obtained results release the classical (AR) condition in some sense.
- difference equation,
- positive solution,
- mountain pass theorem,
- existence,
- nonexistence
Citation: Yuhua Long. Existence and nonexistence of positive solutions to a class of nonlocal discrete Kirchhoff type equations[J]. AIMS Mathematics, 2023, 8(10): 24568-24589. doi: 10.3934/math.20231253

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Abstract

In this paper, we investigate the existence and nonexistence of positive solutions to a class of nonlocal partial difference equations via a variant version of the mountain pass theorem. The conditions in our obtained results release the classical (AR) condition in some sense.

References

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