Journal Of Nonlinear Functional Analysis And Differential Equations

Journal of Nonlinear Functional Analysis and Differential Equations

Linear and Nonlinear Functional Analysis with Applications, Second Edition

This new, considerably expanded edition covers the fundamentals of linear and nonlinear functional analysis, including distribution theory, harmonic analysis, differential geometry, calculus of variations, and degree theory. Numerous applications are included, especially to linear and nonlinear partial differential equations and to numerical analysis. All the basic theorems are provided with complete and detailed proofs. The author has added more than 450 pages of new material; added more than 210 problems; the solutions to all of the problems will be made available on an accompanying website; added two entirely new chapters, one on locally convex spaces and distribution theory and the other on the Fourier transform and Calderón–Zygmund singular integral operators; and enlarged and split the chapter on the “great theorems” of nonlinear functional analysis into two chapters, one on the calculus of variations and the other on Brouwer’s theorem, Brouwer’s degree, and Leray–Schauder’s degree. Ideal for both teaching and self-study, Linear and Nonlinear Functional Analysis with Applications, Second Edition is intended for advanced undergraduate and graduate students in mathematics, university professors, and researchers. It is also an ideal basis for several courses on linear or nonlinear functional analysis.

Nonlinear Functional Analysis with Applications to Combustion Theory

Explore the fascinating intersection of mathematics and combustion theory in this comprehensive monograph, inspired by the pioneering work of N. N. Semenov and D. A. Frank-Kamenetskii. Delving into the nonlinear functional analytic approach, this book examines semilinear elliptic boundary value problems governed by the Arrhenius equation and Newton's law of heat exchange. Key topics include: Detailed analysis of boundary conditions, including isothermal (Dirichlet) and adiabatic (Neumann) cases. Critical insights into ignition and extinction phenomena in stable steady temperature profiles, linked to the Frank-Kamenetskii parameter. Sufficient conditions for multiple positive solutions, revealing the S-shaped bifurcation curves of these problems. Designed for researchers and advanced students, this monograph provides a deep understanding of nonlinear functional analysis and elliptic boundary value problems through their application to combustion and chemical reactor models. Featuring detailed illustrations, clearly labeled figures, and tables, this book ensures clarity and enhances comprehension of complex concepts. Whether you are exploring combustion theory, functional analysis, or applied mathematics, this text offers profound insights and a thorough mathematical foundation.