Positive solutions of IBVPs for $ q $-difference equations with $ p $-Laplacian on infinite interval

Changlong Yu; Jufang Wang; Huode Han; Jing Li; Changlong Yu; Jufang Wang; Huode Han; Jing Li

doi:10.3934/math.2021487

AIMS Mathematics

2021, Volume 6, Issue 8: 8404-8414. doi: 10.3934/math.2021487

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Research article

Positive solutions of IBVPs for $ q $-difference equations with $ p $-Laplacian on infinite interval

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: 16 February 2021 Accepted: 11 May 2021 Published: 31 May 2021
MSC : 39A13, 39A27, 34B40

Nowadays, many researches have considerable attention to the nonlinear $ q $-difference equations boundary value problems as important and useful tool for modeling of different phenomena in various research fields. In this work, we investigate a class of $ q $-difference equations boundary value problems with integral boundary conditions with $ p $-Laplacian on infinite intervals. By applying the Avery-Peterson fixed point theorem in a cone, we establish the existence of three positive solutions for the above boundary value problem. Finally, the main results is illustrated with the aid of an example.
- Avery-Peterson fixed point theorem,
- boundary value problem,
- $ p $-Laplacian operator,
- positive solutions,
- quantum calculus
Citation: Changlong Yu, Jufang Wang, Huode Han, Jing Li. Positive solutions of IBVPs for $ q $-difference equations with $ p $-Laplacian on infinite interval[J]. AIMS Mathematics, 2021, 6(8): 8404-8414. doi: 10.3934/math.2021487

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Abstract

Nowadays, many researches have considerable attention to the nonlinear $ q $-difference equations boundary value problems as important and useful tool for modeling of different phenomena in various research fields. In this work, we investigate a class of $ q $-difference equations boundary value problems with integral boundary conditions with $ p $-Laplacian on infinite intervals. By applying the Avery-Peterson fixed point theorem in a cone, we establish the existence of three positive solutions for the above boundary value problem. Finally, the main results is illustrated with the aid of an example.

References

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