EXISTENCE AND MULTIPLICITY OF WEAK SOLUTIONS FOR A CLASS OF FRACTIONAL STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS WITH IMPULSIVE CONDITIONS

Yan Qiao; Fangqi Chen; Yukun An

doi:10.11948/20190416

2020 Volume 10 Issue 6

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Article navigation > Journal of Applied Analysis & Computation > 2020 > 10(6): 2537-2556

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Yan Qiao, Fangqi Chen, Yukun An. EXISTENCE AND MULTIPLICITY OF WEAK SOLUTIONS FOR A CLASS OF FRACTIONAL STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS WITH IMPULSIVE CONDITIONS[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2537-2556. doi: 10.11948/20190416

Citation:

Yan Qiao, Fangqi Chen, Yukun An. EXISTENCE AND MULTIPLICITY OF WEAK SOLUTIONS FOR A CLASS OF FRACTIONAL STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS WITH IMPULSIVE CONDITIONS[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2537-2556. doi: 10.11948/20190416

EXISTENCE AND MULTIPLICITY OF WEAK SOLUTIONS FOR A CLASS OF FRACTIONAL STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS WITH IMPULSIVE CONDITIONS

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: fangqichen1963@126.com(F. Chen); Email: anykna@nuaa.edu.cn(Y. An)
Fund Project: The authors were supported by National Natural Science Foundation of China (11572148, 11872201)

Abstract

Abstract

In this paper, we consider the existence and multiplicity of weak solutions for a class of fractional differential equations with non-homogeneous Sturm-Liouville conditions and impulsive conditions by using the critical point theory. In addition, at the end of this paper, we also give the existence results of infinite weak solutions of fractional differential equations under homogeneous Sturm-Liouville boundary value conditions. Finally, several examples are given to illustrate our main results.
- Fractional differential equations /
- Sturm-Liouville boundary conditions /
- impulsive conditions /
- critical point theory
MSC: 34A08, 34B15, 34B37

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References

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