Fifth Mississippi State Conference on Differential Equations and Computational Simulations,
Electron. J. Diff. Eqns., Conf. 10, 2003, pp. 11-22.

Monotone method for nonlinear nonlocal hyperbolic problems

Azmy S. Ackleh & Keng Deng

Abstract:
We present recent results concerning the application of the monotone method for studying existence and uniqueness of solutions to general first-order nonlinear nonlocal hyperbolic problems. The limitations of comparison principles for such nonlocal problems are discussed. To overcome these limitations, we introduce new definitions for upper and lower solutions.

Published February 28, 2003.
Subject classifications: 35A05, 35A35, 35L60, 92D99.
Key words: Nonlinear nonlocal hyperbolic IBVP, monotone approximation, existence uniqueness.

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Azmy S. Ackleh
Department of Mathematics
University of Louisiana at Lafayette
Lafayette, Louisiana 70504, USA.
e-mail: ackleh@louisiana.edu
Keng Deng
Department of Mathematics
University of Louisiana at Lafayette
Lafayette, Louisiana 70504, USA.
e-mail: deng@louisiana.edu

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