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Positive solutions to singular second-order boundary value problems. (Chinese. English summary) Zbl 1027.34025
Summary: The author studies the nonlinear boundary value problem \[ u''+ a(t) f(u)= 0,\quad\alpha u(0)-\beta u'(0)= 0,\quad\gamma u(1)+\delta u'(1)= 0, \] where \(a\) is allowed to be singular at both end points \(t= 0\) and \(t=1\) and \(f\) is either superlinear or sublinear. We show the existence of at least one positive solution to this problem.

MSC:
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
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