Asymptotic behavior of positive solutions of $x"=-t^{\alpha \lambda -2}x^{1+\alpha}$ with $\alpha <0$ and $\lambda <-1$ or $\lambda >0$
TSUKAMOTO, Ichiro
Hokkaido Math. J., Tome 36 (2007) no. 4, p. 535-562 / Harvested from Project Euclid
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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 $\lambda <-1$.
Publié le : 2007-08-15
Classification:  asymptotic behavior,  an initial value problem,  the analytical expressions,  a first order rational differential equation,  a two dimensional autonomous system,  34A12,  34A34 
@article{1277472866,
     author = {TSUKAMOTO, Ichiro},
     title = {Asymptotic behavior of positive solutions of $x"=-t^{\alpha \lambda -2}x^{1+\alpha}$ with $\alpha <0$ and $\lambda <-1$ or $\lambda >0$},
     journal = {Hokkaido Math. J.},
     volume = {36},
     number = {4},
     year = {2007},
     pages = { 535-562},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1277472866}
}

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 Math. J., Tome 36 (2007) no. 4, pp.  535-562. http://gdmltest.u-ga.fr/item/1277472866/