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Zbl 0988.34009
Ma, Ruyun; Castaneda, Nelson
Existence of solutions of nonlinear $m$-point boundary-value problems.
(English)
[J] J. Math. Anal. Appl. 256, No.2, 556-567 (2001). ISSN 0022-247X

Let $\xi_i \in (0,1)$, and let $a_i, b_i, i=1,\dots ,m-2$, be positive numbers satisfying the conditions $\sum_{i=1}^{m-2} a_i < 1$, $\sum_{i=1}^{m-2} b_i < 1$. Here, the existence of a positive solution to the multipoint boundary value problem $$u''(t) + a(t) f(u) = 0, \quad t\in (0,1), \qquad u'(0) = \sum_{i=1}^{m-2}b_i u'(\xi_i), \quad u(1)=\sum_{i=1}^{m-2} a_i u(\xi_i),$$ is studied. By using a fixed-point theorem, the existence of a solution is proved if $f(u)$ is either superlinear or sublinear.
[Sabir R.Umarov (Tashkent)]
MSC 2000:
*34B10 Multipoint boundary value problems
34B15 Nonlinear boundary value problems of ODE

Keywords: multipoint boundary value problems; Leray-Schauder continuation theorem; existence of solution

Cited in: Zbl 1154.34016 Zbl 1081.39015

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