Recent Advances in Differential Equations

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.

Table of Contents:
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