Books by V. Lakshmikantham

This volume describes the monotone iterative technique which is used to obtain monotone approximate solutions that converge to the solution of nonlinear problems of partial differential equations of elliptic, parabolic and hyperbolic type.

Detailing the theory of fuzzy differential equations and inclusions and a systematic account of recent developments, this text provides preliminary material of fuzzy set theory; description of calculus for fuzzy functions; an investigation of the basic theory of fuzzy differential equations; and an introduction to fuzzy differential inclusions.

From a modelling point of view, it is more realistic to model a phenomenon by a dynamic system which incorporates both continuous and discrete times, namely, time as an arbitrary closed set of reals called time-scale or measure chain.

This book attempts to put together the works of a wide range of mathematical scientists. It consists of the proceedings of the Seventh Conference on "Nonlinear Analysis and Applications" including papers that were delivered as invited talks and research reports.

Features a theoretical framework to model phenomena with discontinuous changes. This book presents a generalized monotone iterative method in terms of upper and lower solutions appropriate for the study of discontinuous nonlinear differential equations. It also applies this method to derive suitable fixed point theorems in ordered abstract spaces.