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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.
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Details
1 Nanjing University of Aeronautics and Astronautics, Department of Mathematics, Nanjing, China (GRID:grid.64938.30) (ISNI:0000 0000 9558 9911)
2 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)