In this paper, we prove the existence of at least three periodic solutions for the quasilinear periodic boundary value problem \begin{eqnarray} \left\{ \begin{array}{ll} -p(x')x''+\alpha(t)x=\lambda f(t,x) ~{\rm a.e.} ~t\in[0,1], \\ x(1) -x(0)= x'(1)-x'(0)=0 \end{array} \right. \end{eqnarray} under appropriate hypotheses via a three critical points theorem of B. Ricceri. In addition, we give an example to illustrate the validity of our result.

中文翻译：

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拟线性周期边值问题的三个周期解的存在性

在本文中，我们证明了拟线性周期边值问题\ begin {eqnarray} \ left \ {\ begin {array} {ll} -p（x'）x''+ \ alpha至少存在三个周期解（t）x = \ lambda f（t，x）〜{\ rm ae}〜t \ in [0,1]，\\ x（1）-x（0）= x'（1）-x'（ 0）= 0 \ end {array} \ right。通过B. Ricceri的三个临界点定理，在适当的假设下\ end {eqnarray}。另外，我们举一个例子来说明我们的结果的有效性。