We consider the problem of the existence of positive solutions u to the problem , (g ≥ 0,x > 0, n ≥ 2). It is known that if g is nondecreasing then the Osgood condition is necessary and sufficient for the existence of nontrivial solutions to the above problem. We give a similar condition for other classes of functions g.
@article{bwmeta1.element.bwnjournal-article-apmv68z2p177bwm,
author = {Wojciech Mydlarczyk},
title = {A singular initial value problem for the equation $u^{(n)}(x) = g(u(x))$
},
journal = {Annales Polonici Mathematici},
volume = {69},
year = {1998},
pages = {177-189},
zbl = {0903.34003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv68z2p177bwm}
}
Wojciech Mydlarczyk. A singular initial value problem for the equation $u^{(n)}(x) = g(u(x))$
. Annales Polonici Mathematici, Tome 69 (1998) pp. 177-189. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv68z2p177bwm/
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