Recent Advances in Differential Equations

Roberto Conti

• Publisher: Academic Press
• Year: 2014
• ISBN:
  9781483273914
• Topic: Mathematics
• Subtopic: Calculus
• Index: Mathematics

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

• Front Cover
• Recent Advances in Differential Equations
• Copyright Page
• Table of Contents
• Contributors
• Preface
• CHAPTER 1. NONCOOPERATIVE TRAJECTORIES OF n-PERSON DYNAMICAL GAMES AND STABLE NONCOOPERATIVE EQUILIBRIA
• CHAPTER 2. PROCESSUS DE CONTRÔLE AVEC CONTRÔLE INITIAL
• CHAPTER 3. DETERMINATION AND APPLICATION OF VEKUA RESOLVENTS
• CHAPTER 4. GENERALIZED HOPF BIFURCATION
• CHAPTER 5. PERTURBATION OF LINEAR DIFFERENTIAL EQUATIONS BY A HALF-LINEAR TERM DEPENDING ON A SMALL PARAMETER
• CHAPTER 6. ON SOME CAUCHY PROBLEMS ARISING IN COMPUTATIONAL METHODS
• CHAPTER 7. COMPARISON RESULTS AND CRITICALITY IN SOME COMBUSTION PROBLEMS
• CHAPTER 8. BOUNDARY VALUE PROBLEMS FOR PAIRS OF ORDINARY DIFFERENTIAL OPERATORS
• CHAPTER 9. SEMILINEAR ELLIPTIC EQUATIONS AT RESONANCE: HIGHER EIGENVALUES AND UNBOUNDED NONLINEARITIES
• CHAPTER 10. COUNTABLE SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS
• CHAPTER 11. THE ROLE OF THE STRUCTURAL OPERATOR AND THE QUOTIENT SPACE STRUCTURE IN THE THEORY OF HEREDITARY DIFFERENTIAL EQUATIONS
• CHAPTER 12. DEGENERATE EVOLUTION EQUATIONS AND SINGULAR OPTIMAL CONTROL
• CHAPTER 13. COMMUTATIVE LINEAR DIFFERENTIAL OPERATORS
• CHAPTER 14. APPROXIMATIONS OF DELAYS BY ORDINARY DIFFERENTIAL EQUATIONS
• CHAPTER 15. LINEAR STIELTJES INTEGRO-DIFFERENTIAL EQUATIONS
• CHAPTER 16. A CRITICAL STUDY OF STABILITY OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS
• CHAPTER 17. NONLINEAR PERTURBATIONS OF LINEAR PROBLEMS WITH INFINITE DIMENSIONAL KERNEL
• CHAPTER 18. COMPARISON RESULTS FOR REACTION-DIFFUSION EQUATIONS
• CHAPTER 19. ON THE SYNTHESIS OF SOLUTIONS OF INTEGRAL EQUATIONS
• CHAPTER 20. LOCAL EXACT CONTROLLABILITY OF NONLINEAR EVOLUTION EQUATIONS
• CHAPTER 21. TOPOLOGICAL DEGREE AND THE STABILITY OF A CLASS OF VOLTERRA INTEGRAL EQUATIONS
• CHAPTER 22. PERIODIC SOLUTIONS OF SOME NONLINEAR SECOND ORDER DIFFERENTIAL EQUATIONS IN HILBERT SPACES
• CHAPTER 23. OPERATORS OF MONOTONE TYPE AND ALTERNATIVE PROBLEMS WITH INFINITE DIMENSIONAL KERNEL
• CHAPTER 24. STABILITY THEORY FOR COUNTABLY INFINITE SYSTEMS
• CHAPTER 25. A NONLINEAR HYPERBOLIC VOLTERRA EQUATION ARISING IN HEAT FLOW
• CHAPTER 26. LINEARITY AND NONLINEARITYIN THE THEORY OF G-CONVERGENCE
• CHAPTER 27. PATH INTEGRALS AND PARTIAL DIFFERENTIAL EQUATIONS
• CHAPTER 28. ON PERIODIC SOLUTIONS OF HAMILTONIAN SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS
• CHAPTER 29. SOME RESULTS IN FUNCTIONAL INTEGRAL EQUATIONS IN A BANACH SPACE
• CHAPTER 30. TURBULENCE AND HIGHER ORDER BIFURCATIONS
• CHAPTER 31. CONVERGENCE OF POWER SERIES SOLUTIONS OF p-ADIC NONLINEAR DIFFERENTIAL EQUATION
• CHAPTER 32. UNIQUENESS OF PERIODIC SOLUTIONS OF THE LIENARD EQUATION
• CHAPTER 33. BOUNDARY STABILIZABILITY FOR DIFFUSION PROCESSES