In the paper it is shown that each solution $u(r,\alpha)$ ot the initial value problem (2), (3) has a finite limit for $r\rightarrow \infty$, and an asymptotic formula for the nontrivial solution $u(r,\alpha)$ tending to 0 is given. Further, the existence of such a solutions is established by examining the number of zeros of two different solutions $u(r,\bar{\alpha})$, $u(r,\hat{\alpha})$.
@article{104413,
author = {Valter \v Seda and J\'an Pek\'ar},
title = {On some properties of the solution of the differential equation $u''+\frac{2u'}{r}=u-u^3$},
journal = {Applications of Mathematics},
volume = {35},
year = {1990},
pages = {315-336},
zbl = {0719.34058},
mrnumber = {1065005},
language = {en},
url = {http://dml.mathdoc.fr/item/104413}
}
Šeda, Valter; Pekár, Ján. On some properties of the solution of the differential equation $u''+\frac{2u'}{r}=u-u^3$. Applications of Mathematics, Tome 35 (1990) pp. 315-336. http://gdmltest.u-ga.fr/item/104413/
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