Ordinary differential equations in locally convex spaces

Abstract

CONTENTS Introduction §1. Equations with continuous right-hand side 1.1. Some definitions and notation 1.2. Peano's theorem 1.3. Kneser's theorem 1.4. Continuous dependence on initial data 1.5. Joint continuity 1.6. Continuation of solutions 1.7. Picard's theorem 1.8. Some sufficient conditions for the existence of solutions 1.9. Some sufficient conditions for the uniqueness of solutions 1.10. Compactness method §2. Linear equations 2.1. Some definitions and examples 2.2. Continuous dependence on initial data 2.3. Time analyticity of solutions 2.4. Linear equations in sequence spaces 2.5. Linear equations and semigroups of linear operators §3. Equations with smooth right-hand side §4. Linear representations of non-linear equations 4.1. Transition from non-linear equations to linear ones 4.2. Representations of homomorphisms of algebras of continuous and differentiable functions 4.3. Transition from linear equations to non-linear ones References