WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 11, 2012
Positive Solutions of Operator Equations and Nonlinear Beam Equations with a Perturbed Loading Force
Authors: ,
Abstract: In this paper we are concerned with the existence and uniqueness of positive solutions for an operator equation x = Ax + ëBx on an order Banach space, where A and B are nonlinear operators and ë is a parameter. By properties of cones we obtain that there exists a ë* > 0 such that the operator equation has a unique positive solution which is increasing in ë for ë ? [0, ë*], and further, we give an estimate for ë*. In addition, we discuss the existence and uniqueness of positive solutions for an elastic beam equation with three parameters and one perturbed loading force.