Solvability of a Classical Beam Equation With Caratheodory Nonlinearity

In this paper, we study the existence of solutions for a nonlinear fourth-order two-point boundary value problem, where the nonlinear term is a Caratheodory function containing all lower order derivatives of unknown function. In addition, the bounded condition is nonhomogeneous. We obtain a local existence theorem via Leray-Schauder fixed point theorem. In mechanics, the problem describes the deflection of an elastic beam simply supported on the left and clamped on the right by sliding clamps.