Boundary behavior of the unique solution of a one-dimensional problem
In this article, we analyze the blow-up rate of the unique solution to the singular boundary value problem $$\displaylines{ u''(t) =b(t)f(u(t)), \quad u(t)>0, \; t>0, \cr u(0)=\infty, \quad u(\infty)=0, }$$ where f(u) grows more slowly than $u^p$ (p > 1) at infinity, and...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2016-11-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/308/abstr.html |
| Summary: | In this article, we analyze the blow-up rate of the unique
solution to the singular boundary value problem
$$\displaylines{
u''(t) =b(t)f(u(t)), \quad u(t)>0, \; t>0, \cr
u(0)=\infty, \quad u(\infty)=0,
}$$
where f(u) grows more slowly than $u^p$ (p > 1) at infinity,
and $b \in C^{1}(0, \infty)$ which is positive and non-decreasing
(it may vanish at zero). |
|---|---|
| ISSN: | 1072-6691 |