Existence of three periodic solutions for a quasilinear periodic boundary value problem
AIMS Mathematics2020Vol. 5(6), pp. 6061–6072
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Abstract
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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