Electronic Journal of Differential Equations,
Conf. 10 (2002), pp. 11-22.

Title: Monotone method for nonlinear nonlocal hyperbolic problems

Authors: Azmy S. Ackleh (Univ. of Louisiana at Lafayette, LA, USA)
 Keng Deng (Univ. of Louisiana at Lafayette, LA, USA)
 
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.
Math Subject Classifications: 35A05, 35A35, 35L60, 92D99.
Key Words: Nonlinear nonlocal hyperbolic IBVP; monotone approximation;  
existence uniqueness.