Existence of positive solutions for some superlinear fourth-order boundary value problems

We are concerned with the following superlinear fourth-order equation u(4)(t) + u(t) φ (t,u (t)) = 0,t ∈ (0,1); u(0) = u(1) = 0,u′ (0) = a,u′ (1) = -b,where a,b are nonnegative constants such that a + b > 0 and φ (t,s) is a nonnegative continuous function that is required to satisfy some appropriate conditions related to a class script k satisfying suitable integrability condition. our purpose is to prove the existence,uniqueness,and global behavior of a classical positive solution to the above problem by using a method based on estimates on the green function and perturbation arguments. copyright © 2014 i. bachar and h. mâagli.