Global structure of positive solutions for a class of nonlinear second order three point boundary value problems
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O175.8

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    In this paper we consider the second-order three-point boundary value Problem~ \[\begin{cases} u''(t)+h(t)f(u)=0,~~\ \ \ t\in (0,1),\\[2ex] u'(0)=0, ~u(1)=\lambda u(\eta), \end{cases} \] where~$\eta\in[0,1)$,~$\lambda\in[0,1)$~is a parameter,~$f\in C( [0,\infty),[0,\infty))$~satisfies~$f(s)>0$~for $s>0$, and $h\in C( [0,1],[0,\infty))$~is not identically zero on any subinterval of [0,1]. We give information on the interesting problem as to what happens to the norms of positive solutions as $\lambda$ varies in $[0,1)$ under the conditions of~$f_{0}=0,~f_{\infty}=\infty$.~The proof of main result is based upon the fixed point index theory on cone and connectivity properties of the solution set.

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Cite this article as: WEI Li-Ping. Global structure of positive solutions for a class of nonlinear second order three point boundary value problems [J]. J Sichuan Univ: Nat Sci Ed, 2018, 55: 440.

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History
  • Received:October 10,2017
  • Revised:November 20,2017
  • Adopted:November 22,2017
  • Online: March 29,2018
  • Published: