Nonlinear Second Order Elliptic Equations

By: Mingxin Wang, Peter Y. H. Pang

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Hardcover | 13 June 2024

At a Glance

Hardcover
328 Pages

Dimensions(cm)
23.5 x 15.5 x 1.91

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This book focuses on the following three topics in the theory of boundary value problems of nonlinear second order elliptic partial differential equations and systems: (i) eigenvalue problem, (ii) upper and lower solutions method, and (iii) topological degree method. In particular, we mainly concern ourselves with the existence of solutions, more specifically non-constant positive solutions, as well as the uniqueness, stability and asymptotic behavior of such solutions.

While not all-encompassing, these topics represent major approaches to the theory of partial differential equations and systems, and should be of significant value to all graduate students and researchers. Two appendices have been included to provide a good gauge of the prerequisites for this book and make the book reasonably self-contained.

A major strength of the book is that it contains a large number of substantial examples. Exercises for the reader are also included. Therefore, this book is suitable as a textbook for graduate students who have already had an introductory course on PDE and some familiarity with functional analysis and nonlinear functional analysis, but may also serve as a useful reference for researchers.

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