Solvability Of Two Kinds Of Multi-point Boundary Value Problems For Quasilinear Ordinary Differential Equations

The main purpose of this paper is to get results on the solvability of two kinds of multi-point boundary value problems for quasilinear ordinary differential equations by employing Leray-Schauder continuation theorem.The following hypotheses are adopted:H1) is continuous ,strictly increasing and odd, ；H2) be a function satisfying Carathéodory's conditions .H3) , The main results are as follows:1. we concern with the following boundary value problem: (I)Assumed H1),H2),H3)are satisfied, all of the 's havingthe same signs and ,we give sufficient conditions for the solvability of the BVP(I).2. the following boundary value problem is studied: (II)Assumed H1),H2),H3)are satisfied, or ,we give two the existences two the existencestheorems about BVP(II).