In recent years, functional methods have become central to the study of theoretical and applied mathematical problems. As demonstrated in this Research Note, functional methods can not only provide more generality, but they can also unify results and techniques and lead to better results than those obtained by classical methods.
Preliminaries. Elliptic Boundary Value Problems. Parabolic Boundary Value Problems with Algebraic Boundary Conditions. Parabolic Boundary Value Problems with Algebraic-Differential boundary Conditions. Hyperbolic Boundary Value Problems with Algebraic Boundary Conditions. Hyperbolic Boundary Value Problems with Algebraic-Differential boundary conditions. The Fourier Method for Abstract Differential Equations. The Semigroup Approach for Abstract Differential Equations. Nonlinear Non-Autonomous Abstract Differential Equations. Implicit Nonlinear Abstract Differential and Integral Equations.