| Variational Method to the Fractional Impulsive Equation with Neumann Boundary Conditions |
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| 引用本文： | Wei Zhang,Zhongyuan Wang,Jinbo Ni. Variational Method to the Fractional Impulsive Equation with Neumann Boundary Conditions[J]. Journal of Applied Analysis & Computation, 2024, 14(5) |
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| 作者姓名： | Wei Zhang Zhongyuan Wang Jinbo Ni |
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| 摘 要： |
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| 收稿时间： | 2023-12-04 |
| 修稿时间： | 2024-04-04 |
Variational Method to the Fractional Impulsive Equation with Neumann Boundary Conditions |
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| Affiliation: | School of mathematics and big data, Anhui University of Science and Technology, Huainan, Anhui, 232001, PR China,School of mathematics and big data, Anhui University of Science and Technology, Huainan, Anhui, 232001, PR China,School of mathematics and big data, Anhui University of Science and Technology, Huainan, Anhui, 232001, PR China |
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| Abstract: | We study the multiplicity of solutions for a class of fractional differential equations influenced by both instantaneous and non-instantaneous impulses, subject to Neumann boundary conditions. A key contribution of this paper is that we have established a new variational structure and successfully applied critical point theory to investigate the impulsive fractional Neumann boundary value problem. By using the critical point theorem, we give some new criteria to guarantee that the impulsive problem has at least three solutions. An example is also given to illustrate the main results. |
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| Keywords: | Fractional differential equation Instantaneous impulses Non-instantaneous impulses Neumann boundary condition Critical point theorem |
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