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

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} \rig...

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Bibliographic Details
Published inAIMS mathematics Vol. 5; no. 6; pp. 6061 - 6072
Main Authors Wang, Zhongqian, Liu, Dan, Song, Mingliang
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2020
Subjects
critical point
periodic boundary problem
periodic solutions
three solutions
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2020389