Nonlinear Problems with Lack of Compactness

The book is dedicated to the study of elliptic problems when lack of compactness occurs. This research area has been intensively developed in recent years also in connection with nonlinear phenomena that naturally arise in General Topology, Geometric Analysis, Functional and Convex Analysis, Game Theory, Mathematical Economics, and other branches of pure and applied sciences. The main mathematical interest relies on the fact that some classical results of Functional Analysis, mainly based on variational arguments, cannot be directly used for problems with lack of compactness and new techniques have to be produced. The aim of the monograph is to present some of these techniques together with their applications to elliptic problems with variational structure. The current literature on these abstract tools and on their applications is therefore very interesting and quite large. The book is addressed to researchers and post-graduate as well as graduate students for a comprehensive introduction to the existence theory for elliptic partial differential equations with lack of compactness and can serve as a textbook. The extensive reference list and index make it as a reference book.