An existence theorem of solution to a nonlinear cantilever beam equation

Key words:  fourth-order ordinary differential equation  boundary value problem  existence of solution  nonlinear alternative

Abstract:

The existence of solution was considered for a nonlinear fourth-order two-point boundary value problem with all order derivatives. In material mechanics, the problem is called cantilever beam equation which describes the deformations of an elastic beam fixed at left and freed at right. By using Green function and nonlinear alternative, constructing suitable Banach space and applying the technique of integral equation, an existence theorem was obtained for the problem when the nonlinear term satisfies the condition of .functional linear increase.