MATH 627 Differential Equations in Banach Spaces
Mean value theorem for Banach space-valued piecewise differentiable functions, differentiable and Lipschitzian operators, construction of epsilon-approximate solution to a differential equation, existence and uniqueness of local solutions, extensions to a maximal solution. Continuity and differentiability of a solution with respect to initial data and parameters. Linear differential equations in the class of continuous operators, existence and properties of resolvent. Relations with PDEs of first order. Application of the theory to ODEs in concrete Banach spaces. Prerequisites: 540 and 625.