Positive Solutions of Operator Equations and Nonlinear Beam Equations with a Perturbed Loading Force
نویسنده
چکیده
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 ∈ [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. Key–Words: Nonlinear operator equation; positive solution; elastic beam equation; perturbed loading force
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تاریخ انتشار 2012