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.

中文翻译：

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一类带有p- Laplacian分数阶微分方程的非平凡解的变分方法

本文通过变分方法研究了一类带参数的分数阶微分方程的边值问题。首先，我们给出了一个结果，即边值问题在二次条件和超二次条件下分别具有至少一个弱解。此外，我们使用不带Ambrosetti–Rabinowitz条件的著名山口引理得到至少一个非平凡解的存在。最后，通过最近的Bonanno和Marano临界点定理，确定了至少三个解的存在。