Analytical solutions for a class of nonlinear boundary value problems for beam deflection with a small parameter

D. A. Maslov

National Research University Moscow Power Engineering Institute, Moscow, Russian Federation

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.

Keywords: weakly nonlinear problem, small parameter solution, Banach space, boundary value problem.