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 \(f(t,y)\).


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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