Boundary value problems with sublinear conditions near zero

We prove a multiplicity result for the two-point boundary value problem associated to a second order equation of the form ¶¶\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ u'' + {\cal F}(t, u, u') = 0 $\end{document}¶¶ where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ {\cal F} = {\cal F}(t,x,y) $\end{document} satisfies a sublinear condition at x = 0 and no assumption at infinity is required. We use a topological degree method based on a continuation theorem and on the performance of a time-map technique for an autonomous problem.