Differential calculus and equations

The problems of modern society are both complex and inter-disciplinary.

A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and analysis of the physical and biological phenomena they represent.

The book is mainly about hybrid systems with continuous/discrete-time dynamics.

The book provides a comprehensive, detailed and self-contained treatment of the fundamental mathematical properties of problems arising from the motion of viscous incompressible fluids around rotating obstacles.

This book offers the reader an overview of recent developments of integral equations on time scales.

This book offers the reader a new approach to the solvability of boundary value problems with state-dependent impulses and provides recently obtained existence results for state dependent impulsive problems with general linear boundary conditions.

This monograph covers the existing results regarding Green's functions for differential equations with involutions (DEI).

This monograph offers the reader a treatment of the theory of evolution PDEs with nonstandard growth conditions.

The book aims to provide an unifying view of a variety (a 'zoo') of mathematical models with some kind of singular nonlinearity, in the sense that it becomes infinite when the state variable approaches a certain point.

In this monograph the author presents explicit conditions for the exponential, absolute and input-to-state stabilities including solution estimates of certain types of functional differential equations.

This book is a mathematically rigorous introduction to the beautiful subject of ordinary differential equations for beginning graduate or advanced undergraduate students.

The book is devoted to rigorous derivation of macroscopic mathematical models as a homogenization of exact mathematical models at the microscopic level.

This book provides an introduction to age-structured population modeling which emphasizes the connection between mathematical theory and underlying biological assumptions.

This book introduces a variety of neural network methods for solving differential equations arising in science and engineering.

The Lerch zeta-function is the first monograph on this topic, which is a generalization of the classic Riemann, and Hurwitz zeta-functions.

To our wives, Masha and Marian Interest in the so-called completely integrable systems with infinite num- ber of degrees of freedom was aroused immediately after publication of the famous series of papers by Gardner, Greene, Kruskal, Miura, and Zabusky [75, 77, 96, 18, 66, 19J (see also [76]) on striking properties of the Korteweg-de Vries (KdV) equation.

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.