Global invertibility theorems and their applications - a variational approach - Galewski, Marek; Koniorczyk, Marcin (Wydawnictwo Politechnika Łódzka, 2016)
This book is concerned with deriving abstract tools which are applicable in solving integro-differential equations posed in a Banach space setting. Our approach relies on deriving conditions which guarantee that certain mapping acting between two Banach spaces is a diffeomorphim thereby obtaining that if this mapping is a solution operator to some equation then this very equation has a unique solution which in fact is well posed in the sense of Hadamard.(...)
Keywords: przestrzenie Banacha; równania różniczkowe; diffeomorfizmy; Banach spaces; differential equations; diffeomorphim