ArticleOpen Access 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
Published: October 31, 2023
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.
Keyword
Fractional differential equation, integral boundary conditions, coupled system, p-laplacian operator, positive solutions
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Copyright
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How to cite this paper
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 Computation, 7(3), 404-414.
DOI: http://dx.doi.org/10.26855/jamc.2023.09.012