Hokkaido Mathematical Journal

TSUKAMOTO Ichiro,

Asymptotic behavior of positive solutions of $x"=-t^{\alpha \lambda -2}x^{1+\alpha}$ with $\alpha <0$ and $\lambda <-1$ or $\lambda >0$ .

Hokkaido Mathematical Journal, 36 (2007) pp.535-562

Fulltext

PDF

Abstract

In this paper, we consider an initial value problem of the differential equation written in the title under an initial condition $x(T)=A$, $x'(T)=B$ $(00$, we conclude that if $T$ and $A$ are fixed arbitrarily, then there exists a number $B_{1}$ such that in every case of $B = B_{1}$, $B>B_{1}$, and $B0$. Finally we discuss the case $T=0$ and $\lambda <-1$.

MSC(Primary)34A12
MSC(Secondary)34A34
Uncontrolled Keywordsasymptotic behavior, an initial value problem, the analytical expressions, a first order rational differential equation, a two dimensional autonomous system