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On the existence of positive solutions of ordinary differential equations. (English) Zbl 0802.34018
The authors use a fixed point theorem in cones (due to Krasnosel’skij) to prove the existence of positive solutions to the second-order boundary value problem \(u''+ a(t) f(u)= 0\), \(0< t<1\); \(\alpha u(0)- \beta u'(0)= 0\), \(\gamma u(1)+ \delta u'(1)= 0\), where \(a\in C([0,1]; [0,\infty))\) with \(a\not\equiv 0\) on any subinterval of \([0,1]\), \(\alpha,\beta,\gamma,\delta\geq 0\) (with \(\gamma\beta+\alpha\gamma+ \alpha\delta>0\)), and \(f\) is a continuous nonnegative function that is assumed to be either sublinear or superlinear.

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
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