Monotone iterative techniques for discontinuous nonlinear differential equations
By: Seppo Heikkilä, V. Lakshmikantham.
Contributors: Lakshmikantham, V., 1926-
Series: Monographs and textbooks in pure and applied mathematics ;; 181
Publisher: M. Dekker
Published: 1994
Place of publication: New York
Language: eng
Number of pages: 514
Subjects: Differential equations, Nonlinear -- Numerical solutions.; Iterative methods (Mathematics)
Description: Providing the theoretical framework to model phenomena with discontinuous changes, this unique reference presents a generalized monotone iterative method in terms of upper and lower solutions appropriate for the study of discontinuous nonlinear differential equations and applies this method to derive suitable fixed point theorems in ordered abstract spaces.

Detailing the basic concepts behind a generalized monotone iterative method, Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations develops new existence and comparison results when the functions involved in the differential equations admit a threefold decomposition into continuous and discontinuous functions in the dependant variable; extends the method of upper and lower solutions and the monotone iterative technique to Caratheodory systems in finite as well as infinite dimensional spaces; covers the existence and comparison of strong, weak, or mild solutions to discontinuous differential equations in Banach spaces without requiring any compactness hypotheses ; treats first order and second order partial differential equations; and more.
Notes: Includes bibliographical references (p. 489-506) and index.