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Existence and multiplicity of positive solutions of a fourth-order m-piont BVP with sign-changing Green's function
  • Huijuan Zhu,
  • Fanglei Wang,
  • Nannan Yang
Huijuan Zhu
Hohai University
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Fanglei Wang
Hohai University

Corresponding Author:[email protected]

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Nannan Yang
Nanjing University
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In this paper, we study the fourth-order m-point boundary value problem \begin{equation*} \left \{\begin{array}{lcr} u^{(4)}(t)=f(t,u(t)),\ t\in [0,1],\\ u’(0)=u’‘(0)=u(1)=0 , u’‘(1)-\sum^{m-2}_{i=1}\alpha_i u”’(\xi_i)=0, \end{array}\right. \end{equation*} with sign-changing Green’s function. By using some fixed theorems and the properties of Green’s function, we mainly establish the existence and multiplicity of positive solution for the problems under some suitable conditions.