## Positive solutions to superlinear singular boundary value problems.(English)Zbl 0902.34017

In the study of nonlinear phenomena many mathematical models give rise to problems $y''+ q(t) f(t,y)= 0,\quad 0< t< 1,\tag{1}$
$y(0)= y(1)= 0$ with $$q\in C(0,1)$$, $$q>0$$ on $$(0,1)$$, and $$f:[0, 1]\times (0,\infty)\to \mathbb{R}$$ is continuous.
The authors prove the existence of a solution $$y(t)\in C[0,1]\cap C^2(0, 1)$$ with $$y>0$$ on $$(0,1)$$ to the problem (1) if there are some supplementary assumptions on $$q(t)$$ and $$f(t,y)$$.

### MSC:

 34B15 Nonlinear boundary value problems for ordinary differential equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations

### Keywords:

boundary value problems; positive; singular
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### References:

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