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Positive solutions for singular second order three-point boundary value problems. (English) Zbl 1117.34021
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:
34B16Singular nonlinear boundary value problems for ODE
34B10Nonlocal and multipoint boundary value problems for ODE
34B18Positive solutions of nonlinear boundary value problems for ODE
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References:
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