Electron. J. Differential Equations, Vol. 2016 (2016), No. 308, pp. 1-12.

Boundary behavior of the unique solution of a one-dimensional problem

Ling Mi

Abstract:
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).

Submitted June 30, 2015. Published November 30, 2016.
Math Subject Classifications: 35J25, 35J60, 35J65.
Key Words: One-dimensional problems; uniqueness of the solution; boundary behavior.

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Ling Mi
School of Science
Linyi University
Linyi, Shandong 276005, China
email: mi-ling@163.com

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