Monotone Positive Solution of Nonlinear Third-Order BVP with Integral Boundary Conditions

This paper is concerned with the following third-order boundary value problem with integral boundary conditions u'''(t) + f(t, u(t), u'(t)) = 0, t is an element of [0,1]; u(0) = u'(0) = 0,u'(1) = integral(1)(0) g(t)u' (t)dt, where f is an element of C([0,1]) x [0, + infinity) x [0, + infinity), [0, + infinity)) and g is an element of C([0,1], [0, + infinity)). By using the Guo-Krasnoselskii fixed-point theorem, some sufficient conditions are obtained for the existence and nonexistence of monotone positive solution to the above problem.