## Differential and Integral Equations

### Existence of monotone solutions to some singular boundary and initial value problems

L. E. Bobisud

#### Abstract

We establish conditions sufficient to guarantee existence of nondecreasing solutions on $[0,1]$ of the differential equation $y''+f(t,y,y')=0$ subject to the boundary conditions $y(0)=0$, $y(1)=a>0$ or the initial conditions $y(0)=0$, $y'(0)=a>0$. Here $f$ is a nonnegative function which may be singular as $y\downarrow0$.

#### Article information

Source
Differential Integral Equations, Volume 8, Number 8 (1995), 2145-2156.

Dates
First available in Project Euclid: 20 May 2013

https://projecteuclid.org/euclid.die/1369056144

Mathematical Reviews number (MathSciNet)
MR1348969

Zentralblatt MATH identifier
0836.34020

Subjects
Primary: 34B15: Nonlinear boundary value problems
Secondary: 47H15 47N20: Applications to differential and integral equations

#### Citation

Bobisud, L. E. Existence of monotone solutions to some singular boundary and initial value problems. Differential Integral Equations 8 (1995), no. 8, 2145--2156. https://projecteuclid.org/euclid.die/1369056144