- Research Article
- Open access
- Published:
Solvability for a Class of Abstract Two-Point Boundary Value Problems Derived from Optimal Control
Boundary Value Problems volume 2007, Article number: 027621 (2008)
Abstract
The solvability for a class of abstract two-point boundary value problems derived from optimal control is discussed. By homotopy technique existence and uniqueness results are established under some monotonic conditions. Several examples are given to illustrate the application of the obtained results.
References
Lions J-L: Optimal Control of Systems Governed by Partial Differential Equations. Springer, New York, USA; 1971:xi+396.
Hu Y, Peng S: Solution of forward-backward stochastic differential equations. Probability Theory and Related Fields 1995,103(2):273–283. 10.1007/BF01204218
Peng S: Probabilistic interpretation for systems of quasilinear parabolic partial differential equations. Stochastics and Stochastics Reports 1991,37(1–2):61–74.
Wu Z: One kind of two-point boundary value problems associated with ordinary equations and application. Journal of Shandong University 1997, 32: 17–24.
Peng S, Wu Z: Fully coupled forward-backward stochastic differential equations and applications to optimal control. SIAM Journal on Control and Optimization 1999,37(3):825–843. 10.1137/S0363012996313549
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Wang, L. Solvability for a Class of Abstract Two-Point Boundary Value Problems Derived from Optimal Control. Bound Value Probl 2007, 027621 (2008). https://doi.org/10.1155/2007/27621
Received:
Accepted:
Published:
DOI: https://doi.org/10.1155/2007/27621