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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.