Positive solutions for a system of fractional $ q $-difference equations with generalized $ p $-Laplacian operators

Hongyu Li; Liangyu Wang; Yujun Cui; Hongyu Li; Liangyu Wang; Yujun Cui

doi:10.3934/era.2024051

Electronic Research Archive

2024, Volume 32, Issue 2: 1044-1066. doi: 10.3934/era.2024051

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Positive solutions for a system of fractional $ q $-difference equations with generalized $ p $-Laplacian operators

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Received: 17 October 2023 Revised: 05 January 2024 Accepted: 08 January 2024 Published: 24 January 2024

In this paper, we consider the existence of positive solutions for a system of fractional $ q $-difference equations with generalized $ p $-Laplacian operators. By using Guo-Krasnosel'skii fixed point theorem, we obtain some existence results of positive solutions for this system with two parameters under some different combinations of superlinearity and sublinearity of the nonlinear terms. In the end, we give two examples to illustrate our main results.
- fixed point theorem,
- fractional $ q $-difference equation,
- generalized $ p $-Laplacian operator,
- existence,
- positive solution
Citation: Hongyu Li, Liangyu Wang, Yujun Cui. Positive solutions for a system of fractional $ q $-difference equations with generalized $ p $-Laplacian operators[J]. Electronic Research Archive, 2024, 32(2): 1044-1066. doi: 10.3934/era.2024051

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Abstract

In this paper, we consider the existence of positive solutions for a system of fractional $ q $-difference equations with generalized $ p $-Laplacian operators. By using Guo-Krasnosel'skii fixed point theorem, we obtain some existence results of positive solutions for this system with two parameters under some different combinations of superlinearity and sublinearity of the nonlinear terms. In the end, we give two examples to illustrate our main results.

References

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