V. Lakshmikantham 
Nonlinear Equations in Abstract Spaces [PDF ebook] 
Proceedings of an International Symposium on Nonlinear Equations in Abstract Spaces, Held at the University of Texas at Arlington, Arlington, Texas, June 8-10, 1977

Many problems in partial differential equations which arise from physical models can be considered as ordinary differential equations in appropriate infinite dimensional spaces, for which elegant theories and powerful techniques have recently been developed. This book gives a detailed account of the current state of the theory of nonlinear differential equations in a Banach space, and discusses existence theory for differential equations with continuous and discontinuous right-hand sides. Of special importance is the first systematic presentation of the very important and complex theory of multivalued discontinuous differential equations.