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Positive solutions to a multi-point higher order boundary value problem. (English) Zbl 1101.34004
The authors study existence and nonexistence of positive solutions to the higher order multi-point boundary value problem $$u^{(n)}(t)+\lambda g(t)f(u(t))=0,$$ $$u(0)=u'(0)=\cdots =u^{(n-2)}(0)=0,\quad \sum^m_{i=1}a_i u^{(n-2)}(\xi_i)=u^{(n-2)}(1),$$ with $a_i>0, \ i=1, \cdots, m$, $\sum^m_{i=1}a_i=1$, and $\frac1 2\leq \xi_1<\cdots<\xi_m<1$. For related results, see {\it R. Ma} and {\it L. Ren} [Appl. Math. Lett. 16, 863-869 (2003; Zbl 1070.34039)].

MSC:
34B10Nonlocal and multipoint boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
34B18Positive solutions of nonlinear boundary value problems for ODE
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References:
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