In this note we consider the boundary value problem $y''=f(x,y,y')$ $\,(x\in [0,X];X>0)$, $y(0)=0$, $y(X)=a>0$; where $f$ is a real function which may be singular at $y=0$. We prove an existence theorem of positive solutions to the previous problem, under different hypotheses of Theorem 2 of L.E. Bobisud [J. Math. Anal. Appl. 173 (1993), 69–83], that extends and improves Theorem 3.2 of D. O'Regan [J. Differential Equations 84 (1990), 228–251].
@article{118790,
author = {Gabriele Bonanno},
title = {An existence theorem of positive solutions to a singular nonlinear boundary value problem},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {36},
year = {1995},
pages = {609-614},
zbl = {0847.34020},
mrnumber = {1378684},
language = {en},
url = {http://dml.mathdoc.fr/item/118790}
}
Bonanno, Gabriele. An existence theorem of positive solutions to a singular nonlinear boundary value problem. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 609-614. http://gdmltest.u-ga.fr/item/118790/
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