### AIMS Mathematics

2020, Issue 6: 6061-6072. doi: 10.3934/math.2020389
Research article

# Existence of three periodic solutions for a quasilinear periodic boundary value problem

• Received: 02 June 2020 Accepted: 15 July 2020 Published: 24 July 2020
• MSC : 34B15, 34C25, 70H12

• 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.

Citation: Zhongqian Wang, Dan Liu, Mingliang Song. Existence of three periodic solutions for a quasilinear periodic boundary value problem[J]. AIMS Mathematics, 2020, 5(6): 6061-6072. doi: 10.3934/math.2020389

### Related Papers:

• 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.

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