SOLVABILITY OF NONLINEAR ORDINARY DIFFERENTIAL EQUATION WHEN ITS ASSOCIATED LINEAR EQUATION HAS NO NONTRIVIAL OR SIGN-CHANGING SOLUTION

Abstract

In this paper we investigate the existence of nontrivial solutions of a two-point boundary value problem. Under the condition that the associated linear boundary value problem has no nontrivial solutions or no sign-changing solutions and some other additional conditions, we prove some existence theorems of (nontrivial) solutions.