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Oscillation Theory for Difference and Functional Differential Equations (Hardcover, 2000 ed.)
Loot Price: R3,077
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Oscillation Theory for Difference and Functional Differential Equations (Hardcover, 2000 ed.)
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This monograph is devoted to a rapidly developing area of research
of the qualitative theory of difference and functional differential
equations. In fact, in the last 25 years Oscillation Theory of
difference and functional differential equations has attracted many
researchers. This has resulted in hundreds of research papers in
every major mathematical journal, and several books. In the first
chapter of this monograph, we address oscillation of solutions to
difference equations of various types. Here we also offer several
new fundamental concepts such as oscillation around a point,
oscillation around a sequence, regular oscillation, periodic
oscillation, point-wise oscillation of several orthogonal
polynomials, global oscillation of sequences of real valued
functions, oscillation in ordered sets, ( , R, )-oscillate,
oscillation in linear spaces, oscillation in Archimedean spaces,
and oscillation across a family. These concepts are explained
through examples and supported by interesting results. In the
second chapter we present recent results pertaining to the oscil
lation of n-th order functional differential equations with
deviating argu ments, and functional differential equations of
neutral type. We mainly deal with integral criteria for
oscillation. While several results of this chapter were originally
formulated for more complicated and/or more general differ ential
equations, we discuss here a simplified version to elucidate the
main ideas of the oscillation theory of functional differential
equations. Further, from a large number of theorems presented in
this chapter we have selected the proofs of only those results
which we thought would best illustrate the various strategies and
ideas involved."
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