## Singular boundary value problems for superlinear second order ordinary and delay differential equations.(English)Zbl 0863.34022

The authors study the existence of solutions for the following singular boundary value problems for nonlinear second order ordinary and delay differential equations: $\begin{cases} y''(t)+ q(t)f(t,y(t))=0, &0<t<1,\\ y(0)= y(1)=0;\end{cases} \tag{1}$
$\begin{cases} {1\over{p(t)}} (p(t)y'(t))'+ q(t)f(t,y(t))=0, &0<t<1,\\ {\displaystyle {\lim_{t\searrow 0}}} p(t)y'(t)= y(1)=0;\end{cases} \tag{2}$
$\begin{cases} y''(t)+ q(t)f(t,y(t-r))=0, &t\in(0;1) \setminus\{r\},\\ y(t)= \mu(t), &t\in[-r;0],\\y(1)=0, &0<r<1,\;r=\text{const}.\end{cases} \tag{3}$ {}.

### MSC:

 34B15 Nonlinear boundary value problems for ordinary differential equations 34K10 Boundary value problems for functional-differential equations
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