Boundary value problems with sublinear conditions near zero

Abstract.

We prove a multiplicity result for the two-point boundary value problem associated to a second order equation of the form ¶¶$u'' + {\cal F}(t, u, u') = 0$¶¶ where ${\cal F} = {\cal F}(t,x,y)$ 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.