Positive solutions of some nonlocal 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 nonlocal BVP Green function. The existence of at least one positive solutions for the nonlocal fourth-order boundary value problem with the first order derivative u~(4) (t)+ Au"(t) = λf (t, u(t), u(t)), 0 < t < 1 u(0) = u(1) = ∫_0~1 p(s)u(s)ds u"(0) = u"(1) = ∫_0~1 q(s)u" (s)ds is considered, where f is a nonnegative continuous function and λ > 0,0 < A < π~2, p, q ∈ L [0,1], p(s) ≥ 0, q(s) ≤ 0.