Global structure of positive solutions for third-order semipositone integral boundary value problems

In this paper, we were concerned with the global behavior of positive solutions for thirdorder semipositone problems with an integral boundary condition y ''' + beta y '' + alpha y ' + lambda f(t,y) = 0, t is an element of (0, 1), y(0) = y '(0) = 0, y(1) = chi integral(1 )(0)y(s)ds, 0 where alpha is an element of (0, infinity) and beta is an element of (-infinity, infinity) are two constants, lambda, chi are two positive parameters, and f is an element of C([0, 1] x [0, infinity), R) with f(t, 0) < 0. Our analysis mainly relied on the bifurcation theory.