EXISTENCE OF SOLUTIONS FOR FRACTIONAL DIFFERENTIAL EQUATION WITH <i>P</i>-LAPLACIAN THROUGH VARIATIONAL METHOD

Dongping Li; Fangqi Chen; Yukun An

doi:10.11948/2018.1778

2018 Volume 8 Issue 6

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Dongping Li, Fangqi Chen, Yukun An. EXISTENCE OF SOLUTIONS FOR FRACTIONAL DIFFERENTIAL EQUATION WITH P-LAPLACIAN THROUGH VARIATIONAL METHOD[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1778-1795. doi: 10.11948/2018.1778

Citation:

Dongping Li, Fangqi Chen, Yukun An. EXISTENCE OF SOLUTIONS FOR FRACTIONAL DIFFERENTIAL EQUATION WITH P-LAPLACIAN THROUGH VARIATIONAL METHOD[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1778-1795. doi: 10.11948/2018.1778

EXISTENCE OF SOLUTIONS FOR FRACTIONAL DIFFERENTIAL EQUATION WITH P-LAPLACIAN THROUGH VARIATIONAL METHOD

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

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Abstract

Abstract

In this paper, a class of fractional differential equation with p-Laplacian operator is studied based on the variational approach. Combining the mountain pass theorem with iterative technique, the existence of at least one nontrivial solution for our equation is obtained. Additionally, we demonstrate the application of our main result through an example.
- Fractional differential equation /
- p-Laplacian operator /
- variational method /
- mountain pass theorem /
- iterative technique
MSC: 26A33;34B15;35A15

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References

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