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Existence and nonexistence for a singular boundary value problem. (English) Zbl 0628.34025
Existence of positive solutions of the two-point boundary value problem $$y''=\lambda ^ 2f(x,y)$$, $$y(0)=a>0$$, $$y(1)=b\geq 0$$ is studied, where $$\lambda ^ 2>0$$ and $$\int _{0}f(x,y)dy<\infty$$ but $$\lim _{y\to 0}f(x,y)=\infty.$$ It is shown that positive solutions exist provided $$\lambda ^ 2$$ is sufficiently small but that no positive solutions exist for $$\lambda ^ 2$$ large.

##### MSC:
 34B15 Nonlinear boundary value problems for ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations
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##### References:
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