Differential calculus and equations

The history of martingale theory goes back to the early fifties when Doob [57] pointed out the connection between martingales and analytic functions.

Approach your problems from the It isn't that they can't see the end and begin with the answers.

In the last century many problems which arose in the science, engineer- ing and technology literature involved nonlinear complex phenomena.

This book considers some models described by means of partial dif- ferential equations and boundary conditions with chaotic stochastic disturbance.

During the last twenty-five years, the development of the theory of Banach lattices has stimulated new directions of research in the theory of positive operators and the theory of semigroups of positive operators.

A decade has passed since Problems of Nonlinear Deformation, the first book by E.

It was noted in the preface of the book "e;Inequalities Involving Functions and Their Integrals and Derivatives"e;, Kluwer Academic Publishers, 1991, by D.

Oscillation theory was born with Sturm's work in 1836.

In this monograph, the authors present a compact, thorough, systematic, and self-contained oscillation theory for linear, half-linear, superlinear, and sublinear second-order ordinary differential equations.

The nonlinear normal modes of a parametrically excited cantilever beam are constructed by directly applying the method of multiple scales to the governing integral-partial differential equation and associated boundary conditions.

For seventy years, we have known that Einstein's theory is essentially a theory of propagation of waves for the gravitational field.

This book is about the light like (degenerate) geometry of submanifolds needed to fill a gap in the general theory of submanifolds.

The present monograph is devoted to the complex theory of differential equations.

The role of Hilbert polynomials in commutative and homological algebra as well as in algebraic geometry and combinatorics is well known.

The aim of this book is a detailed study of topological effects related to continuity of the dependence of solutions on initial values and parameters.

In 1909 Alfred Haar introduced into analysis a remarkable system which bears his name.

Nonlinear difference equations of order greater than one are of paramount impor- tance in applications where the (n + 1)st generation (or state) of the system depends on the previous k generations (or states).

Scale is a concept the antiquity of which can hardly be traced.

Gauge theory, symplectic geometry and symplectic topology are important areas at the crossroads of several mathematical disciplines.

Beginning with the works of N.

We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems.

The last fifty years have witnessed several monographs and hundreds of research articles on the theory, constructive methods and wide spectrum of applications of boundary value problems for ordinary differential equations.

It was long ago that group analysis of differential equations became a powerful tool for studying nonlinear equations and boundary value problems.

As is well-known, a control system always works under a variety of accidental or continued disturbances.

It is generally acknowledged that deterministic formulations of dy- namical phenomena in the social sciences need to be treated differently from similar formulations in the natural sciences.

There seems to be two types of books on inequalities.

There are many problems in nonlinear partial differential equations with delay which arise from, for example, physical models, biochemical models, and social models.

Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary differential equations.

Boundary value problems for partial differential equations playa crucial role in many areas of physics and the applied sciences.

Conventional digital computation methods have run into a se- rious speed bottleneck due to their serial nature.

Functional Equations, Inequalities and Applications provides an extensive study of several important equations and inequalities, useful in a number of problems in mathematical analysis.

Methods in Nonlinear Integral Equations presents several extremely fruitful methods for the analysis of systems and nonlinear integral equations.

Two-and three-level difference schemes for discretisation in time, in conjunction with finite difference or finite element approximations with respect to the space variables, are often used to solve numerically non- stationary problems of mathematical physics.

The asymptotic theory deals with the problern of determining the behaviour of a function in a neighborhood of its singular point.

In this book we study sprays and Finsler metrics.

Despite their novelty, wavelets have a tremendous impact on a number of modern scientific disciplines, particularly on signal and image analysis.

Historically, complex analysis and geometrical function theory have been inten- sively developed from the beginning of the twentieth century.

It seems hard to believe, but mathematicians were not interested in integration problems on infinite-dimensional nonlinear structures up to 70s of our century.

The present monograph analyses the FitzHugh-Nagumo (F-N) model Le.

Preface to the English Edition The present monograph is a revised and enlarged alternative of the author's monograph [19] which was devoted to the development of a unified approach to studying differential inclusions, whose values of the right hand sides are compact, not necessarily convex subsets of a Banach space.

Iteration regularization, i.

To summarize briefly, this book is devoted to an exposition of the foundations of pseudo differential equations theory in non-smooth domains.

This book is devoted to one of the main questions of the theory of extremal prob- lems, namely, to necessary and sufficient extremality conditions.

The material of the present book is an extension of a graduate course given by the author at the University "e;Al.