Positive solutions of operator equations and nonlinear beam quations with a perturbed loading force

Authors:
Wen-Xia Wang;Xi-Lan Liu
Affiliations:
Taiyuan Normal University, Department of Mathematics, Taiyuan, P. R. China;Shanxi Datong University, Department of mathematics and Computational Science, Datong, P. R. China
Venue:
WSEAS Transactions on Mathematics
Year:
2012

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Abstract

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 λ 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 ε [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.