Positive solutions of a nonlinear higher order boundary-value problem

Abstract

The authors consider the higher order boundary-value problem $$displaylines{ u^{(n)}(t)= q(t)f(u(t)), quad 0 leq t leq 1, cr u^{(i-1)}(0) = u^{(n-2)}(p) = u^{(n-1)}(1)=0, quad 1 leq i leq n-2, }$$ where $nge 4$ is an integer, and $pin(1/2,1)$ is a constant. Sufficient conditions for the existence and nonexistence of positive solutions of this problem are obtained. The main results are illustrated with an example.