ITERATIVE SOLUTIONS FOR SOME FOURTH-ORDER PERIODIC BOUNDARY VALUE PROBLEMS

Abstract

In this paper, by using a new maximum principle and the Fredholm alternative, the monotone method in the presence of lower and upper solutions for the periodic problem $$ \begin{array}{rl} u^{(iv)}(x) & \hspace{-0.2cm} = f(x,u(x),u^{\prime\prime}(x)) , \ \ 0\lt x \lt 2 \pi , \\ u^{(i)}(0)& \hspace{-0.2cm} =u^{(i)}(2 \pi) , \ \ i=0, 1, 2, 3 \end{array} $$ is developed, where $f:[0, 2 \pi] \times R^2 \longrightarrow R$ is a Caratheodory function.