Analytical Solutions for a Class of Nonlinear Boundary Value Problems for Beam Deflection with a Small Parameter

Abstract

we investigated a class of weakly nonlinear boundary value problems in perturbation theory that arise in the mathematical modeling of beam deflection on a nonlinear elastic foundation. We formulated the problem as an equation in a Banach space, where a linear differential operator is perturbed by a polylinear bounded operator. We obtained sufficient conditions for the existence of an analytical solution for a small parameter and identified the corresponding range of parameter values. We also proposed a method for constructing this solution.