## Differential and Integral Equations

### On the exact number of solutions of a singular boundary-value problem

#### Abstract

In this paper, we investigate the exact number of positive solutions of the Dirichlet boundary-value problem $u''-u^{-\gamma}+\beta=0$. We will show that the exact number of positive solutions can be 2, 1, 0, depending on the length of the interval and $\gamma$. This solves some open problems posed in [1].

#### Article information

Source
Differential Integral Equations, Volume 22, Number 7/8 (2009), 787-796.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019548

Mathematical Reviews number (MathSciNet)
MR2532121

Zentralblatt MATH identifier
1240.34106

#### Citation

Horváth, Tamás L.; Simon, Péter L. On the exact number of solutions of a singular boundary-value problem. Differential Integral Equations 22 (2009), no. 7/8, 787--796. https://projecteuclid.org/euclid.die/1356019548