Translator Disclaimer
February 2009 On asymptotic behavior of positive solutions of $x''=-t^{\alpha\lambda-2}x^{1+\alpha}$ with $\alpha\lt 0$ and $\lambda=0, -1$
Ichiro TSUKAMOTO
Hokkaido Math. J. 38(1): 153-175 (February 2009). DOI: 10.14492/hokmj/1248787009

Abstract

Given an initial condition $x(T)=A$, $x'(T)=B$ ($'=d/dt$, $0\lt T \lt \infty$, $0 \lt A \lt \infty$, $-\infty \lt B \lt \infty$) for the differential equation denoted in the title, we shall conclude that if $T$, $A$ are fixed arbitrarily, then there exists a number $B_{\ast}$ such that in every case of $B=B_{\ast}$, $B \lt B_{\ast}$, $B \gt B_{\ast}$ we determine analytical expressions of the solution of the initial value problem which shows asymptotic behavior of the solution. That is, these analytical expressions are valid in neighborhoods of ends of the domain of the solution. If $\lambda =-1$, then we shall treat the case $T=0$, since there exists the solution continuable to $t=0$.

Citation

Download Citation

Ichiro TSUKAMOTO. "On asymptotic behavior of positive solutions of $x''=-t^{\alpha\lambda-2}x^{1+\alpha}$ with $\alpha\lt 0$ and $\lambda=0, -1$." Hokkaido Math. J. 38 (1) 153 - 175, February 2009. https://doi.org/10.14492/hokmj/1248787009

Information

Published: February 2009
First available in Project Euclid: 28 July 2009

zbMATH: 1177.34069
MathSciNet: MR2501899
Digital Object Identifier: 10.14492/hokmj/1248787009

Subjects:
Primary: 34A12
Secondary: 34A34

Rights: Copyright © 2009 Hokkaido University, Department of Mathematics

JOURNAL ARTICLE
23 PAGES


SHARE
Vol.38 • No. 1 • February 2009
Back to Top