Existence and uniqueness criteria for nonlinear quantum difference equations with $ p $-Laplacian

Changlong Yu; Jing Li; Jufang Wang; Changlong Yu; Jing Li; Jufang Wang

doi:10.3934/math.2022582

AIMS Mathematics

2022, Volume 7, Issue 6: 10439-10453. doi: 10.3934/math.2022582

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Existence and uniqueness criteria for nonlinear quantum difference equations with $ p $-Laplacian

Changlong Yu ^{1,2
,
,},
Jing Li ^{1
,
,},
Jufang Wang ²

1.
Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, Beijing 100124, China
2.
College of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, Hebei, China

Received: 11 October 2021 Revised: 28 February 2022 Accepted: 13 March 2022 Published: 28 March 2022
MSC : 34B40, 39A13, 39A27

Q-calculus plays an extremely important role in mathematics and physics, especially in quantum physics, spectral analysis and dynamical systems. In recent years, many scholars are committed to the research of nonlinear quantum difference equations. However, there are few works about the nonlinear $ q- $difference equations with $ p $-Laplacian. In this paper, we investigate the solvability for nonlinear second-order quantum difference equation boundary value problem with one-dimensional $ p $-Laplacian via the Leray-Schauder nonlinear alternative and some standard fixed point theorems. The obtained theorems are well illustrated with the aid of two examples.
- quantum calculus,
- nonlinear quantum difference equations,
- $ p $-Laplacian operator,
- Leray-Schauder nonlinear alternative,
- fixed point theorem
Citation: Changlong Yu, Jing Li, Jufang Wang. Existence and uniqueness criteria for nonlinear quantum difference equations with $ p $-Laplacian[J]. AIMS Mathematics, 2022, 7(6): 10439-10453. doi: 10.3934/math.2022582

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Abstract

Q-calculus plays an extremely important role in mathematics and physics, especially in quantum physics, spectral analysis and dynamical systems. In recent years, many scholars are committed to the research of nonlinear quantum difference equations. However, there are few works about the nonlinear $ q- $difference equations with $ p $-Laplacian. In this paper, we investigate the solvability for nonlinear second-order quantum difference equation boundary value problem with one-dimensional $ p $-Laplacian via the Leray-Schauder nonlinear alternative and some standard fixed point theorems. The obtained theorems are well illustrated with the aid of two examples.

References

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