VARIATIONAL METHODS FOR A FRACTIONAL ADVECTION-DISPERSION EQUATION WITH INSTANTANEOUS AND NON-INSTANTANEOUS IMPULSES AND NONLINEAR STURM-LIOUVILLE CONDITIONS

Yan Qiao; Fangqi Chen; Yukun An

doi:10.11948/20230340

2024 Volume 14 Issue 3

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Article navigation > Journal of Applied Analysis & Computation > 2024 > 14(3): 1698-1716

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Yan Qiao, Fangqi Chen, Yukun An. VARIATIONAL METHODS FOR A FRACTIONAL ADVECTION-DISPERSION EQUATION WITH INSTANTANEOUS AND NON-INSTANTANEOUS IMPULSES AND NONLINEAR STURM-LIOUVILLE CONDITIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1698-1716. doi: 10.11948/20230340

Citation:

Yan Qiao, Fangqi Chen, Yukun An. VARIATIONAL METHODS FOR A FRACTIONAL ADVECTION-DISPERSION EQUATION WITH INSTANTANEOUS AND NON-INSTANTANEOUS IMPULSES AND NONLINEAR STURM-LIOUVILLE CONDITIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1698-1716. doi: 10.11948/20230340

VARIATIONAL METHODS FOR A FRACTIONAL ADVECTION-DISPERSION EQUATION WITH INSTANTANEOUS AND NON-INSTANTANEOUS IMPULSES AND NONLINEAR STURM-LIOUVILLE CONDITIONS

1.
School of Mathematical Sciences, Jiangsu Second Normal University, Nanjing 211200, China
2.
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

Author Bio: Email: fangqichen1963@126.com(F. Chen); Email: anykna@nuaa.edu.cn(Y. An)
Corresponding author: Email: Qiaoyan9192@126.com(Y. Qiao)
Fund Project: The authors were supported by National Natural Science Foundation of China (Grant Nos. 12301185, 11872201, 12172166) and Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 22KJB110013)

Abstract

Abstract

In this paper, a class of fractional advection-dispersion equations with instantaneous and non-instantaneous impulses and nonlinear Sturm-Liouville boundary conditions is considered. Firstly, based on the problem, we define an appropriate function space and construct corresponding variational structures. Then, under weaker conditions than the Ambrosetti-Rabinowitz condition, the existence and multiplicity of solutions to the equation are proven through the Mountain Pass Lemma and genus properties. Finally, an example is provided to illustrate the results obtained in this paper.
- Fractional advection-dispersion equations /
- instantaneous and non-instantaneous impulses /
- nonlinear Sturm-Liouville conditions /
- variational methods
MSC: 34A08, 34A34, 34B15, 34B60

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References

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