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Zbl 1117.34021
Liu, Bingmei; Liu, Lishan; Wu, Yonghong
Positive solutions for singular second order three-point boundary value problems.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 66, No. 12, A, 2756-2766 (2007). ISSN 0362-546X

Summary: The singular three-point boundary value problem $$\cases u''(t)+h (t)f(t,u)=0,\quad 0<t<1,\\ u(0)=0,\quad u(1)=\alpha u(\eta), \endcases$$ where $\eta\in(0,1)$, $0<\alpha<1/\eta$, is considered under some conditions concerning the first eigenvalue corresponding to the relevant linear operator, $h(t)$ is allowed to be singular at $t=0,1$ and $f$ may be singular at $u=0$. The existence of a positive solution is obtained by a fixed-index point.
MSC 2000:
*34B16 Singular nonlinear boundary value problems
34B10 Multipoint boundary value problems
34B18 Positive solutions of nonlinear boundary value problems

Keywords: three point; singular; positive solution; theory of fixed point index

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