VARIATIONAL FORMULATION FOR THE STURM-LIOUVILLE PROBLEM OF FRACTIONAL DIFFERENTIAL EQUATION WITH GENERALIZED (<i>P</i>, <i>Q</i>)-LAPLACIAN OPERATOR

Dongping Li; Yankai Li; Fangqi Chen; Yukun An

doi:10.11948/20220004

2023 Volume 13 Issue 3

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Article navigation > Journal of Applied Analysis & Computation > 2023 > 13(3): 1225-1238

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Dongping Li, Yankai Li, Fangqi Chen, Yukun An. VARIATIONAL FORMULATION FOR THE STURM-LIOUVILLE PROBLEM OF FRACTIONAL DIFFERENTIAL EQUATION WITH GENERALIZED (P, Q)-LAPLACIAN OPERATOR[J]. Journal of Applied Analysis & Computation, 2023, 13(3): 1225-1238. doi: 10.11948/20220004

Citation:

Dongping Li, Yankai Li, Fangqi Chen, Yukun An. VARIATIONAL FORMULATION FOR THE STURM-LIOUVILLE PROBLEM OF FRACTIONAL DIFFERENTIAL EQUATION WITH GENERALIZED (P, Q)-LAPLACIAN OPERATOR[J]. Journal of Applied Analysis & Computation, 2023, 13(3): 1225-1238. doi: 10.11948/20220004

VARIATIONAL FORMULATION FOR THE STURM-LIOUVILLE PROBLEM OF FRACTIONAL DIFFERENTIAL EQUATION WITH GENERALIZED (P, Q)-LAPLACIAN OPERATOR

1.
Department of Mathematics, Xi'an Technological University, Xi'an 710021, China
2.
School of Automation and Information Engineering, Xi'an University of Technology, Xi'an 710048, China
3.
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

Author Bio: Email: li_dongping@126.com(D. Li); Email: fangqichen@nuaa.edu.cn(F. Chen); Email: anykna@nuaa.edu.cn(Y. An)
Corresponding author: Email: liyankai@xaut.edu.cn(Y. Li)
Fund Project: The authors were supported by National Natural Science Foundation of China (12101481, 62103327), Shaanxi Fundamental Science Research Project for Mathematics and Physics (22JSQ022), Young Talent Fund of Association for Science and Technology in Shaanxi, China (20220529), Young Talent Fund of Association for Science and Technology in Xi'an, China (095920221344)

Abstract

Abstract

In this paper, the Sturm-Liouville boundary value problem is studied for fractional differential equation with generalized (p, q)-Laplacian operator. By imposing mild assumptions on nonlinearity f, several new existence results of at least one or two nontrivial weak solutions are established through variational methods and critical point theorems. Furthermore, the criteria is also investigated for the nonexistence result.
- Fractional differential equation /
- Sturm-Liouville boundary value problem /
- variational method
MSC: 26A33, 34B15, 35A15

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