Positive solutions of a nonlinear elastic beam equation rigidly fastened on the left and simply supported on the right

Abstract

The purpose of this paper is to establish several local existence theorems concerned with n positive solutions for a fourth-order two-point boundary value problem, where n is an arbitrary positive integer and the nonlinear term may be singular. In mechanics, the problem describes deflection of an elastic beam rigidly fastened on the left and simply supported on the right.