We study a nonlocal boundary value problem for the equation x''(t) + f(t,x(t),x'(t)) = 0, t ∈ [0,1]. By applying fixed point theorems on appropriate cones, we prove that this boundary value problem admits positive solutions with slope in a given annulus. It is remarkable that we do not assume f≥0. Here the sign of the function f may change.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-3-5,
author = {P. Ch. Tsamatos},
title = {Positive solutions with given slope of a nonlocal second order boundary value problem with sign changing nonlinearities},
journal = {Annales Polonici Mathematici},
volume = {83},
year = {2004},
pages = {231-242},
zbl = {1108.34016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-3-5}
}
P. Ch. Tsamatos. Positive solutions with given slope of a nonlocal second order boundary value problem with sign changing nonlinearities. Annales Polonici Mathematici, Tome 83 (2004) pp. 231-242. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-3-5/