This paper surveys a number of recent results obtained by C. Bereanu and the author in existence results for second order differential equations of the form (ϕ(u'))' = f(t,u,u') submitted to various boundary conditions. In the equation, ϕ: ℝ → ≤ ]-a,a[ is a homeomorphism such that ϕ(0) = 0. An important motivation is the case of the curvature operator, where ϕ(s) = s/√(1+s²). The problems are reduced to fixed point problems in suitable function space, to which Leray-Schauder theory is applied.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc77-0-15,
author = {J. Mawhin},
title = {Boundary value problems for nonlinear perturbations of some ph-Laplacians},
journal = {Banach Center Publications},
volume = {75},
year = {2007},
pages = {201-214},
zbl = {1129.34010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc77-0-15}
}
J. Mawhin. Boundary value problems for nonlinear perturbations of some ϕ-Laplacians. Banach Center Publications, Tome 75 (2007) pp. 201-214. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc77-0-15/