Positive solutions to singular sublinear three-point boundary value problems of second order for ordinary differential equations. (Chinese. English summary) Zbl 1235.34082
Summary: By constructing lower and upper solutions a sufficient condition for the existence of \(C[0,1]\) positive solutions is given for the singular boundary value problem
\[
\begin{cases} x''(t)+f(t,x(t))=0,\;t\in(0,1);\\ x(0)=0, x(1)=kx(\eta),\end{cases}
\]
where \(\eta\in(0,1)\) is a constant, \(f\in C((0,1)\times[0,\infty)\), \([0,\infty))\).
MSC:
| 34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |
| 34B16 | Singular nonlinear boundary value problems for ordinary differential equations |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
