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International Conference on Differential Equations
International Conference on Differential Equations (1974 : University of Southern California)
Front Cover; International Conference on Differential Equations; Copyright Page; Table of Contents; INVITED ADDRESSES AND RESEARCH REPORTS; CONTRIBUTED PAPERS; PREFACE; PART 1:INVITED ADDRESSES AND RESEARCH REPORTS; CHAPTER 1. CONTINUOUS EXTENSIONS: THEIR CONSTRUCTION AND THEIR APPLICATION IN THE THEORY OF DIFFERENTIAL EQUATIONS; REFERENCES; CHAPTER 2. BOUNDARY CONTROL, OF THE DIFFUSION EQUATION A SEMIGROUP THEORETICAL APPROACH; CHAPTER 3. AN ABSTRACT FRAMEWORK FOR APPROXIMATE SOLUTIONS TO OPTIMAL CONTROL PROBLEMS GOVERNED BY HEREDITARY SYSTEMS; 1. Introduction.
2. Abstract representation for solutions of FDEs3. The approximating system and convergence results; 4. Application to optimal control problems; REFERENCES; CHAPTER 4. LOWER CLOSURE AND EXISTENCE THEOREMS IN OPTIMAL CONTROL; 1. Introduction; 2. Notation and Formulation of Problem; 3. Outline of Proof of Existence; 4. Lower Closure Theorems; 6. Outline of Proof; REFERENCES; CHAPTER 5.A SINGULAR CAUCHY PROBLEM AND GENERALIZED TRANSLATIONS; 0. Introduction; 1. The singular Cauchy problem; 2. Estimates for the solution of the Cauchy problem; 3. Generalized translations; REFERENCES.
CHAPTER 6. SOME MODELS FOR POPULATION GROWTH WITH HARVESTINGREFERENCES; CHAPTER 7. THE PROBLEM OF HILL FOR SYSTEMS; 1. Preliminary Results; 2. Periodic Solutions and Characteristic Exponents; CONCLUSIONS; REFERENCES; CHAPTER 8. ALTERNATIVE METHODS IN NONLINEAR ANALYSIS; 1. A canonic decomposition; 2. The auxiliary equation and Banach s fixed point theorem; 3. Applications to ordinary differential equations; 4. Mawhin's work on periodic solutions and extension to general equations with Fredholm operators; 5. Application to ordinary differential equations in the complex field.
6. Application to periodic solutions of nonlinear hyperbolic partial differential equations7. Monotone and maximal monotone operators; 8. Auxiliary equation and monotone maps; 9. Schauder's principle of invariance of domain; 10. The auxiliary equation and Schauder's principle; 11. Application to oscillations of conservative systems; 12. A nonlinear problem in potential theory and general elliptic boundary value problems; 13. Strong nonlinearities; REFERENCES; CHAPTER 9. MINIMUM PRINCIPLES AND POSITIVE SOLUTIONS FOR A CLASS OF NONLINEAR DIFFUSION PROBLEMS; 1. Introduction.
2. Notation and Assumptions3. Basic Lemmas; 4. A Nonlinear Diffusion Operator; 5. A Priori Bounds and Positivity; 6. Application: Enzyme Diffusion-Kinetics; 7. Application: Gas-Lubricated Slider Bearing; REFERENCES; CHAPTER 10. DIAGONALIZATION METHOD IN SINGULAR PERTURBATIONS; 1. Introduction; 2. Diagonalization; 3. Statement and Proof of Theorem 1; 4. A Converse Result; REFERENCES; CHAPTER 11. EIGENFUNCTION EXPANSIONS FOR SELFADJOINT SUBSPACES GENERATED BY SYMMETRIC ORDINARY DIFFERENTIAL OPERATORS; 1. Introduction; 2. The Basic Operator and Its Selfadjoint Sub space Extensions; 3. Eigenfunction Expansions.
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Includes bibliographical references and index.
International Conference on Differential Equations, University of Southern California, 1974.