Nonlinear Functional Analysis and Elliptic Equations

This monograph presents aspects of nonlinear functional analysis used in the study of boundary value problems and illustrates their application to nonlinear elliptic equations. The first two chapters establish foundations such as the functional framework of Lebesgue and Sobolev spaces as well as generalized Orlicz spaces, regularity theory, maximum principles and critical point theory. Building on this groundwork, Chapters 3 and 4 then cover problems with balanced and with unbalanced growth, respectively, which include superlinear problems, logistic and singular equations, sublinear and resonant problems. Each chapter concludes with bibliographical remarks that guide further study and research. Written for graduate students embarking on doctoral research and for researchers working in nonlinear partial differential equations, this volume serves as both an advanced textbook and a valuable reference.