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 existence of solutions to infinite
interval problems. This has resulted in widely applicable results. This
monograph is a cumulation mainly of the authors' research over a period
of more than ten years and offers easily verifiable existence criteria
for differential, difference and integral equations over the infinite
interval. An important feature of this monograph is that we illustrate
almost all the results with examples. The plan of this monograph is as
follows. In Chapter 1 we present the existence theory for second order
boundary value problems on infinite intervals. We begin with several
examples which model real world phenom- ena. A brief history of the
infinite interval problem is also included. We then present general
existence results for several different types of boundary value
problems. Here we note that for the infinite interval problem only two
major approaches are available in the literature.
