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Positive solutions to a second-order multi-point boundary-value problem. (English) Zbl 0964.34022
The Leray-Schauder fixed-point theorem is used to prove the existence of positive solutions to the multipoint boundary value problem \[ u''+ \lambda a(t) f(u,u')= 0, \]
\[ u(0)= 0,\quad u(1)= \sum^{m-2}_{i=1} a_i u(\xi_i), \] under suitable conditions, where ‘\(a\)’ is a continuous function which is allowed to change sign on \([0,1]\), \(f\) is continuous with \(f(0,0)> 0\) and \(\lambda\) is a small positive constant. These results improve the results in [ibid. 1999, No. 34, 1-8 (1999; Zbl 0926.34009)].

MSC:
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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