Abstract

In this paper, a class of boundary value problems for fractional differential equations with a parameter is studied via the variational methods. Firstly, we present a result that the boundary value problems have at least one weak solution under the quadratic condition and the superquadratic condition, respectively. Additionally, we obtain the existence of at least one nontrivial solution by using the famous mountain pass lemma without the Ambrosetti–Rabinowitz condition. Finally, by a recent critical points theorem of Bonanno and Marano, the existence of at least three solutions is established.

Details

Title
Nontrivial solutions of a class of fractional differential equations with p-Laplacian via variational methods
Author
Qiao, Yan 1 ; Chen Fangqi 2 ; An Yukun 1 

 Nanjing University of Aeronautics and Astronautics, Department of Mathematics, Nanjing, China (GRID:grid.64938.30) (ISNI:0000 0000 9558 9911) 
 Nanjing University of Aeronautics and Astronautics, Department of Mathematics, Nanjing, China (GRID:grid.64938.30) (ISNI:0000 0000 9558 9911); Shandong University of Science and Technology, College of Mathematics and Systems Science, Qingdao, China (GRID:grid.412508.a) (ISNI:0000 0004 1799 3811) 
Publication year
2020
Publication date
Dec 2020
Publisher
Hindawi Limited
ISSN
16872762
e-ISSN
16872770
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2384397853
Copyright
Boundary Value Problems is a copyright of Springer, (2020). All Rights Reserved. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.