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)


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


Zbl 1070.34039
Full Text: DOI


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