Recent Advances in Differential Equations

1st Edition - January 28, 1981
Editor: Roberto Conti
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 7 3 9 1 - 4

Recent Advances in Differential Equations contains the proceedings of a meeting held at the International Center for Theoretical Physics in Trieste, Italy, on August 24-28, 1978… Read more

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Recent Advances in Differential Equations contains the proceedings of a meeting held at the International Center for Theoretical Physics in Trieste, Italy, on August 24-28, 1978 under the auspices of the U.S. Army Research Office. The papers review the status of research in the field of differential equations (ordinary, partial, and functional). Both theoretical aspects (differential operators, periodic solutions, stability and bifurcation, asymptotic behavior of solutions, etc.) and problems arising from applications (reaction-diffusion equations, control problems, heat flow, etc.) are discussed. Comprised of 33 chapters, this book first examines non-cooperative trajectories of n-person dynamical games and stable non-cooperative equilibria, followed by a discussion on the determination and application of Vekua resolvents. The reader is then introduced to generalized Hopf bifurcation; some Cauchy problems arising in computational methods; and boundary value problems for pairs of ordinary differential operators. Subsequent chapters focus on degenerate evolution equations and singular optimal control; stability of neutral functional differential equations; local exact controllability of nonlinear evolution equations; and turbulence and higher order bifurcations. This monograph will be of interest to students and practitioners in the field of mathematics.

Contributors

Preface

Noncooperative Trajectories of n-Person Dynamical Games and Stable Noncooperative Equilibria

Processus de Contrôle avec Contrôle Initial

Determination and Application of Vekua Resolvents

Generalized Hopf Bifurcation

Perturbation of Linear Differential Equations by a Half-Linèar Term Depending on a Small Parameter

On Some Cauchy Problems Arising in Computational Methods

Comparison Results and Critically in Some Combustion Problems

Boundary Value Problems for Pairs of Ordinary Differential Operators

Semilinear Elliptic Equations at Resonance: Higher Eigenvalues and Unbounded Nonlinearities

Countable Systems of Ordinary Differential Equations

The Role of the Structural Operator and the Quotient Space Structure in the Theory of Hereditary Differential Equation

Degenerate Evolution Equations and Singular Optimal Control

Commutative Linear Differential Operators

Approximations of Delays by Ordinary Differential Equations

Linear Stieltjes Integro-Differential Equations

A Critical Study of Stability of Neutral Functional Differential Equations

Nonlinear Perturbations of Linear Problems with Infinite Dimensional Kernel

Comparison Results for Reaction-Diffusion Equations

On the Synthesis of Solutions of Integral Equations

Local Exact Controllability of Nonlinear Evolution Equations

Topological Degree and the Stability of a Class of Volterra Integral Equations

Periodic Solutions of Some Nonlinear Second Order Differential Equations in Hilbert Spaces

Operators of Monotone-Type and Alternative Problems with Infinite Dimensional Kernel

Stability Theory for Countably Infinite Systems

A Nonlinear Hyperbolic Volterra Equation Arising in Heat Flow

Linearity and Nonlinearity in the Theory of G-Convergence

Path Integrals and Partial Differential Equations

On Periodic Solutions of Hamiltonian Systems of Ordinary Differential Equations

Some Results in Functional Integral Equations in a Banach Space

Turbulence and Higher Order Bifurcations

Convergence of Power Series Solutions of p-Adic Nonlinear Differential Equation

Uniqueness of Periodic Solutions of the Lienard Equation

Boundary Stabilizability for Diffusion Processes