Singular boundary value problems for superlinear second order ordinary and delay differential equations (Q1815651)

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