THE EXISTENCE OF POSITIVE SOLUTIONS FOR A SEMIPOSITONE SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEM

Abstract

In this paper, we study the existence of positive solutions to boundary value problem

{u '' + lambda f(t,u)=0, t is an element of(0,1);

u(0)=Sigma(m-2)(i-1) alpha (i)u(xi(i)), u'(1) = Sigma (m-2)(i=1) beta(i) u'(xi(i)),

where xi(i) is an element of(0, 1), 0 < xi(1) < xi(2) < ... < xi(m-2) < 1, alpha(i), beta(i) is an element of[0,infinity), lambda is positive parameter. By using Krasnoserskii's fixed point theorem, we provide sufficient conditions for the existence of at least one positive solution to the above boundary value problem.