The author considers the following nonlinear fourth-order boundary-value problem with non-homogeneous boundary conditions:
where are given constants and is a given continuous function. In mechanics, the problem () describes the equilibrium state of an elastic beam simply supported at left and clamped at right by sliding clamps. An improved iterative sequence is constructed by the help of monotonic technique which approximates successively the solution of the problem () under suitable assumptions. The function is said to be Carathéodory if
for a. e. , is continuous,
for all , is measurable and
for every , there exists a non-negative function such that , .
An example is presented to illustrate the result obtained.