Existence and uniqueness of solutions for a second-order iterative boundary-value problem
Date
2018-08-08
Authors
Kaufmann, Eric R.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider the existence and uniqueness of solutions to the second-order iterative boundary-value problem
x″(t) = ƒ(t, x(t), x[2](t)), α ≤ t ≤ b,
where x[2](t) = x(x(t)), with solutions satisfying one of the boundary conditions x(α) = α, x(b) = b or x(α) = b, x(b) = α. The main tool employed to establish our results is the Schauder fixed point theorem.
Description
Keywords
Iterative differential equation, Schauder fixed point theorem, Contraction mapping principle
Citation
Kaufmann, E. R. (2018). Existence and uniqueness of solutions for a second-order iterative boundary-value problem. <i>Electronic Journal of Differential Equations, 2018</i>(150), pp. 1-6.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.