Nonlinear Differential Equations

Nonlinear Differential Equations

Invariance, Stability, and Bifurcation

1st Edition - January 1, 1981

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  • Editors: Piero de Mottoni, Luigi Salvadori
  • eBook ISBN: 9781483262499

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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


    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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