Asymptotic Analysis

In this book we present the main results on the asymptotic theory of ordinary linear differential equations and systems where there is a small parameter in the higher derivatives. We are concerned with the behaviour of solutions with respect to the parameter and for large values of the independent variable. The literature on this question is considerable and widely dispersed, but the methods of proofs are sufficiently similar for this material to be put together as a reference book. We have restricted ourselves to homogeneous equations.

This book is a survey of asymptotic methods set in the current applied research context of wave propagation. It stresses rigorous analysis in addition to formal manipulations. Asymptotic expansions developed in the text are justified rigorously, and students are shown how to obtain solid error estimates for asymptotic formulae.

Many real-world problems in science and engineering, including physical, biological, and social phenomena, can be mathematically formulated and rigorously solved by modeling them in linear and nonlinear differential and partial differential equations. This Special Issue titled “Differential Equations and Asymptotic Analysis: Recent Advances and Applications” consists of a collection of papers written by eminent mathematicians and experts in their fields, covering many different areas of nonlinear analysis, both theoretical and applied, related to differential equations, including fixed point theory, monotone operator theory, equilibrium problems and optimization, asymptotic analysis, mathematical biology, and numerical computations. We hope that this Special Issue will be of interest to many researchers, as well as graduate students working in these fields.