We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t, y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = 0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In...
We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is re...
The theory of integral and integrodifferential equations has ad vanced rapidly over the last twenty years. Of course the question of existence is an age-old problem of major importance. This mono graph is a collection of some of the most advanced results to date in this field. The book is organized as follows. It is divided into twelve chap ters. Each chapter surveys a major area of research. Specifically, some of the areas considered are Fredholm and Volterra integral and integrodifferential equations, resonant and nonresonant problems, in tegral inclusions, stochastic equations and periodic...
The theory of integral and integrodifferential equations has ad vanced rapidly over the last twenty years. Of course the question of existence is an a...
Infinite interval problems abound in nature and yet until now there has been no book dealing with such problems. The main reason for this seems to be that until the 1970's for the infinite interval problem all the theoretical results available required rather technical hypotheses and were applicable only to narrowly defined classes of problems. Thus scientists mainly offer d and used special devices to construct the numerical solution assuming tacitly the existence of a solution. In recent years a mixture of classical analysis and modern fixed point theory has been employed to study the...
Infinite interval problems abound in nature and yet until now there has been no book dealing with such problems. The main reason for this seems to be ...
In the last century many problems which arose in the science, engineer- ing and technology literature involved nonlinear complex phenomena. In many situations these natural phenomena give rise to (i). ordinary differ- ential equations which are singular in the independent and/or dependent variables together with initial and boundary conditions, and (ii). Volterra and Fredholm type integral equations. As one might expect general exis- tence results were difficult to establish for the problems which arose. Indeed until the early 1990's only very special examples were examined and these examples...
In the last century many problems which arose in the science, engineer- ing and technology literature involved nonlinear complex phenomena. In many si...
In analysing nonlinear phenomena many mathematical models give rise to problems for which only nonnegative solutions make sense. In the last few years this discipline has grown dramatically. This state-of-the-art volume offers the authors' recent work, reflecting some of the major advances in the field as well as the diversity of the subject. Audience: This volume will be of interest to graduate students and researchers in mathematical analysis and its applications, whose work involves ordinary differential equations, finite differences and integral equations.
In analysing nonlinear phenomena many mathematical models give rise to problems for which only nonnegative solutions make sense. In the last few years...
This work is dedicated to Professor V. Lakshmikantham on the occasion of his 80th birthday. The volumes consist of 45 research papers from distinguished experts from a variety of research areas. Topics include monotonicity and compact methods, blow up and global existence for hyperbolic problems, dynamic systems on time scales, maximum monotone mappings, fixed point theory, quasivalued elliptic problems including mixed BVP's, impulsive and evolution inclusions, iterative processes, Morse theory, hemivariational inequalities, Navier-Stokes equations, multivalued BVP's, various aspects of...
This work is dedicated to Professor V. Lakshmikantham on the occasion of his 80th birthday. The volumes consist of 45 research papers from distinguish...
