Nonlinear Functional Analysis and Elliptic Equations

Erscheinungsjahr 2027
ISBN: 978-3-032-45496-6
Verlag: Springer

Buch, Englisch, 809 Seiten, Format (B × H): 155 mm x 235 mm

Reihe: Springer Monographs in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Papageorgiou, Nikolaos S.

Zeng, Shengda

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Chapter 1. Mathematical Background.- Chapter 2. Boundedness and Hölder Continuity.- Chapter 3. Problems with Balanced Growth.- Chapter 4. Unbalanced Growth Problems.

Über Autor(innen)

Nikolaos S. Papageorgiou is a professor of mathematics at the National Technical University in Athens, Greece. He got his B.S. in Mathematics and in Electrical Engineering from MIT and his PhD in Applied Mathematics from Harvard University. His areas of interest include nonlinear analysis, partial differential equations, optimal control, and mathematical economics.

Vicen?iu D. Radulescu is a State Professor (title awarded by the President of Poland) at the AGH University of Kraków and a professor at the Brno University of Technology. He got his PhD at the Sorbonne University in 1995 under the coordination of Professor Haim Brezis and his Habilitation in 2003 at the Sorbonne University and the AGH University of Kraków in 2023. In 2024, he received the Award of the Prime Minister of Poland for highly advanced research in mathematics. He is a corresponding member of the Accademia Peloritana dei Pericolanti and the Accademia delle Scienze dell'Umbria. His research interests are at the interplay between elliptic PDEs, nonlinear analysis and the calculus of variations.  

Shengda Zeng is a professor at the National Center for Applied Mathematics in Chongqing, Chongqing Normal University, Chongqing, China. He got his PhD in January 2020 at the Faculty of Mathematics and Computer Science in Jagiellonian University, Kraków, Poland. His research interests cover differential equations, nonlinear functional analysis, methods and techniques of nonlinear analysis, calculus of variations, control theory, identification, homogenization, mathematical modeling of physical systems, applications of PDEs to problems of mechanics. He has authored around 100 papers which have been indexed by Google Scholar, resulting in an h-Index of 34 and over 3,305 citations.