Let G and f:[0,1]×ℝ4→ℝ be two functions satisfying Caratheodory conditions. This paper is
concerned with the problems of existence and uniqueness of
solutions for the nonlinear fourth-order ordinary differential
equation y′′′′+λy′′+ky+G(x,y,y′,y′′,y′′′)=f(x,y,y′,y′′,y′′′) with one of a particular set of boundary
conditions.