Location：Home / Journals / Article Detail

Journal of Applied Mathematics and Computation

DOI：http://dx.doi.org/10.26855/jamc.2023.09.012

# Positive Solutions for a System of p-Laplacian Equation Involving Integral Boundary Conditions

Xiujuan Wang*, Tingting Xue, Yuanbing Liu

School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi, Xinjiang, China.

*Corresponding author: Xiujuan Wang

Date: October 31,2023　Hits: 320

### Abstract

In this paper, we discuss the existence of positive solutions of a coupled system of p-laplacian fractional differential equations with integral boundary conditions. In this paper, we show some necessary deﬁnitions and lemmas, with doubling measure and in (quasi-)Banach function spaces. We find that the properties of Banach function spaces and the condition are used to get the conclusion, which is just the same as the conditions of the estimate of the functions in Theorem 1.1. Particularly, the condition could be seen as a separation condition in combining the given lemmas, we obtain important properties of Green's function associated with the fractional BVP. Thus, by Theorem 3.2, the FBVP has no positive solution. According to the properties of Green's function, by using Guo-Krasnosel' skii fixed point theorem on cones, we prove the existence, uniqueness, multiplicity results, and nonexistence of positive solutions for fractional boundary value problems. Finally, an example is provided to illustrate our main result.

### References

[1] Xingqin Zhang, Lin Wang. Existence of positive solutions for a class of nonlinear equation with integral boundary conditions [J]. Math Anal Appl., 2014, 226: 708-718.

[2] Xinguang Zhang. The eigenvalue for a class of singular p-Laplacian fractional differential equation involving the Riemann-Stieltjes integral boundary conditions [J]. Math Anal Appl., 2014, 235: 412-422.

[3] Wengui Yang. Positive solutions for a couple system of nonlinear equation with integral boundary conditions [J]. Math Anal Appl. 2012, 63:288-297.

[4] Johnny Henderson. Positive Solutions for a system of fractional differential equation with coupled integral boundary conditions [J]. Math. Anal. Appl., 2014, 249: 182-197.

[5] Ning Wang, Zongfu Zhou. Positive Solutions of Boundary Value Problem for Fractional Diﬀerential Coupled Systems with p-Laplacian [J]. Mathematica applicata, 2023, 36(2):530-539

[6] Yuehan Liu, Xiaodi Zhao, Huihui Pang. Positive Solutions to a Coupled Fractional Diﬀerential System with p-Laplacian Operator [J]. Discrete Dynamics in Nature and Society, 2019(5):1-12.

[7] Rao, Sabbavarapu Nageswara. Multiplicity of positive solutions for coupled system of fractional diﬀerential equation with p-Laplacian two-point BVPs [J]. Journal of Applied Mathematics and Computing, 2017, 55(1):41-58.

[8] Amina Mahdjouba, Juan J. Nieto, Abdelghani Ouahab. System of fractional boundary value problem with p-Laplacian and advanced arguments [J]. Advances in Difference Equations, 2021(1):1-22.

[9] K Zhang, J Xu, D O'Regan. Positive solutions for a coupled system of nonlinear fractional differential equations [J]. Mathematical Methods in the Applied Sciences, 2014, 16(1):177-193.

[10] Sun J X. Nonlinear Functional Analysis and it’s Application [M]. Science Press, Beijing, 2008.

[11] K. B. Oldham, J. Spanier, The Fractional Calculus [M]. Academic Press, New York, 1974.

### Full-Text HTML

Positive Solutions for a System of p-Laplacian Equation Involving Integral Boundary Conditions

How to cite this paper: Xiujuan Wang, Tingting Xue, Yuanbing Liu. (2023) Positive Solutions for a System of p-Laplacian Equation Involving Integral Boundary Conditions. Journal of Applied Mathematics and Computation7(3), 404-414.

DOI: http://dx.doi.org/10.26855/jamc.2023.09.012