Existence theorems of positive solutions to a class of singular second order boundary value problems of the form y'' + f(x,y,y') = 0, 0 < x < 1, are established. It is not required that the function (x,y,z) → f(x,y,z) be nonincreasing in y and/or z, as is generally assumed. However, when (x,y,z) → f(x,y,z) is nonincreasing in y and z, some of O'Regan's results [J. Differential Equations 84 (1990), 228-251] are improved. The proofs of the main theorems are based on a fixed point theorem for weakly sequentially continuous operators.
@article{bwmeta1.element.bwnjournal-article-apmv64z3p237bwm,
author = {Gabriele Bonanno},
title = {Positive solutions to nonlinear singular second order boundary value problems},
journal = {Annales Polonici Mathematici},
volume = {63},
year = {1996},
pages = {237-251},
zbl = {0867.34014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv64z3p237bwm}
}
Gabriele Bonanno. Positive solutions to nonlinear singular second order boundary value problems. Annales Polonici Mathematici, Tome 63 (1996) pp. 237-251. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv64z3p237bwm/
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