POSITIVE SOLUTIONS FOR A <i>P</i>-LAPLACIAN TYPE SYSTEM OF IMPULSIVE FRACTIONAL BOUNDARY VALUE PROBLEM$ ^* $

Dongping Li; Fangqi Chen; Yukun An

doi:10.11948/20190131

2020 Volume 10 Issue 2

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Dongping Li, Fangqi Chen, Yukun An. POSITIVE SOLUTIONS FOR A P-LAPLACIAN TYPE SYSTEM OF IMPULSIVE FRACTIONAL BOUNDARY VALUE PROBLEM$ ^* $[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 740-759. doi: 10.11948/20190131

Citation:

Dongping Li, Fangqi Chen, Yukun An. POSITIVE SOLUTIONS FOR A P-LAPLACIAN TYPE SYSTEM OF IMPULSIVE FRACTIONAL BOUNDARY VALUE PROBLEM$ ^* $[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 740-759. doi: 10.11948/20190131

POSITIVE SOLUTIONS FOR A P-LAPLACIAN TYPE SYSTEM OF IMPULSIVE FRACTIONAL BOUNDARY VALUE PROBLEM$ ^* $

1.
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
2.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Corresponding authors: Email address: li_dongping@126.com (D. Li); Email address: fangqichen@nuaa.edu.cn (F. Chen); Email address: anykna@nuaa.edu.cn (Y. An)
Fund Project: This work is supported by the National Natural Science Foundation of China(Nos. 11872201, 11572148), the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX18_0242) and the Nanjing University of Aeronautics and Astronautics PhD short-term visiting scholar project(No. 190108DF08)

Abstract

Abstract

In this paper, the aim is to discuss a class of p-Laplacian type fractional Dirichlet's boundary value problem involving impulsive impacts. Based on the approaches of variational method and the properties of fractional derivatives on the reflexive Banach spaces, the existence results of positive solutions for our equations are established. Two examples are given at the end of each main result.
- Fractional differential system /
- p-Laplacian operator /
- positive solution /
- variational method
MSC: 26A33, 34B15, 35A15

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References

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