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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
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References:

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