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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 R. Ma and L. Ren [Appl. Math. Lett. 16, 863-869 (2003; Zbl 1070.34039)].
Reviewer: Ruyun Ma (Lanzhou)

##### MSC:
 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 47H10 Fixed-point theorems 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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