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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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##### References:
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