Positive Solutions of Operator Equations and Nonlinear Beam Equations with a Perturbed Loading Force

摘要

In this paper we are concerned with the existence and uniqueness of positive solutions for an operator equation x = Ax + λBx on an order Banach space, where A and B are nonlinear operators and A is a parameter. By properties of cones we obtain that there exists a λ~* > 0 such that the operator equation has a unique positive solution which is increasing in λ for λ ∈ [0, λ~*], and further, we give an estimate for λ~*. In addition, we discuss the existence and uniqueness of positive solutions for an elastic beam equation with three parameters and one perturbed loading force.