Positive solutions of the fourth-order boundary value problem with dependence on the first order derivative

摘要

In this paper, By the use of a new fixed point theorem and the Green function. The existence of at least one positive solutions for the fourth-order boundary value problem with the first order derivative {u~((4)) (t) + Au" (t) = λ f (t, u(t), u'(t)) 0 < t < 1 u(0) = u(1) = u" (0) = u"(1) = 0 is considered, where f is a nonnegative continuous function and λ > 0, 0 < A < π~2.