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Positive solutions for a singular second-order three-point boundary value problem. (English) Zbl 1138.34015
Summary: This paper is concerned with the existence of positive solutions for the singular three-point boundary value problem $$u''(t)+a(t)u'(t)+b(t)u(t)+h(t)f(t,u)=0,\quad 0<t<1\quad u(0)=0,\quad u(1)=\alpha u(\eta),$$ where $h(t)$ is allowed to be singular at $t=0,1$ and $f$ may be singular at $u = 0$. Existence criteria for positive solutions are established by applying the fixed point index theorem under some weaker conditions concerning the first eigenvalue corresponding to the relevant linear operator.

MSC:
34B18Positive solutions of nonlinear boundary value problems for ODE
34B10Nonlocal and multipoint boundary value problems for ODE
34B16Singular nonlinear boundary value problems for ODE
47H11Degree theory (nonlinear operators)
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References:
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