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"The book is very well written and will be a valuable source for specialists in differential equations, functional analysis, operator theory, and mathematical physics, as well as for non-specialists who want to get an idea of this fascinating field of contemporary nonlinear analysis. The authors have achieved a double goal. On the one hand, they provide a self-contained account which describes the state-of-the-art of nonlinear elliptic equations with degenerations and singularities; on the other, their book will certainly stimulate further research in this field. The reviewer regards the second aspect as at least as important as the first one: in fact, in his opinion a book should open a new field, rather than close it." Zentralblatt für Mathematik