Nonlinear Differential Equations
Invariance, Stability, and Bifurcation
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Nonlinear Differential Equations: Invariance, Stability, and Bifurcation presents the developments in the qualitative theory of nonlinear differential equations. This book discusses the exchange of mathematical ideas in stability and bifurcation theory. Organized into 26 chapters, this book begins with an overview of the initial value problem for a nonlinear wave equation. This text then focuses on the interplay between stability exchange for a stationary solution and the appearance of bifurcating periodic orbits. Other chapters consider the development of methods for ascertaining stability and boundedness and explore the development of bifurcation and stability analysis in nonlinear models of applied sciences. This book discusses as well nonlinear hyperbolic equations in further contributions, featuring stability properties of periodic and almost periodic solutions. The reader is also introduced to the stability problem of the equilibrium of a chemical network. The final chapter deals with suitable spaces for studying functional equations. This book is a valuable resource for mathematicians.
Table of Contents
Contributors
Preface
Abstract Nonlinear Wave Equations: Existence, Linear, and Multilinear Cases, Approximation, Stability
Stability Problems of Chemical Networks
Stability and Generalized Hopf Bifurcation through a Reduction Principle
Almost Periodicity and Asymptotic Behavior for the Solutions of a Nonlinear Wave Equation
Differentiability of the Solutions with respect to the Initial Conditions
Some Remarks on Boundedness and Asymptotic Equivalence of Ordinary Differential Equations
Periodic Solutions for a System of Nonlinear Differential Equations Modelling the Evolution of Oro-Faecal Diseases
Generalized Hopf Bifurcation
Boundary Value Problems for Nonlinear Differential Equations on Non-Compact Intervals
The Electric Ballast Resistor: Homogeneous and Nonhomogeneous Equilibria
Equilibria of an Age-Dependent Population Model
A Variation-of-Constants Formula for Nonlinear Volterra Integral Equations of Convolution Type
An Example of Bifurcation in Hydrostatics
Some Existence and Stability Results for Reaction-Diffusion Systems with Nonlinear Boundary Conditions
On the Asymptotic Behavior of the Solutions of the Nonlinear Equation x+h(t,x) x+p2(t)f(x)=0.
Numerical Methods for Nonlinear Boundary Value Problems at Resonance
On Orbital Stability and Center Manifolds
A Bunch of Stationary or Periodic Solutions near an Equilibrium by a Slow Exchange of Stability
Periodic and Nonperiodic Solutions of Reversible Systems
Some Problems of Reaction-Diffusion Equations
The Role of Quasisolutions in the Study of Differential Equations
Semilinear Equations of Gradient Type in Hilbert Spaces and Applications to Differential Equations
Sur la Decomposition Asymptotique des Systemes Differentiels Fondee sur des Transformations de Lie
Bifurcation of Periodic Solutions for Some Systems with Periodic Coefficients
Global Attractivity for Diffusion Delay Logistic Equations
On Suitable Spaces for Studying Functional Equations Using Semigroup Theory
Product details
- No. of pages: 370
- Language: English
- Copyright: © Academic Press 1981
- Published: January 1, 1981
- Imprint: Academic Press
- eBook ISBN: 9781483262499
About the Editors
Piero de Mottoni
Luigi Salvadori
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