03647nam a22005535i 4500 978-981-99-8692-7 DE-He213 20251030112014.0 cr nn 008mamaa 240426s2024 si | s |||| 0|eng d 9789819986927 978-981-99-8692-7 10.1007/978-981-99-8692-7 doi QA370-380 PBKJ bicssc MAT007000 bisacsh PBKJ thema Wang, Mingxin. author. aut http://id.loc.gov/vocabulary/relators/aut 75856 Nonlinear Second Order Elliptic Equations [electronic resource] / by Mingxin Wang, Peter Y. H. Pang. 1st ed. 2024. Singapore : Springer Nature Singapore : Imprint: Springer, 2024. XII, 314 p. 29 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Preface -- Preliminaries -- Eigenvalue problems of second order linear elliptic operators -- Upper and lower solutions method for single equations -- Upper and lower solutions method for systems -- Theory of topological degree in cones and applications -- Systems with homogeneous Neumann boundary conditions -- P-Laplace equations and systems -- Appendix A: Basic results of Sobolev spaces and nonlinear functional analysis -- Appendix B: Basic theory of elliptic equations -- References -- Index. 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, (iii) topological degree method, and deals 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 interest to graduate students and researchers. Two appendices have been included to provide a good gauge of the prerequisites for this book and make it reasonably self-contained. A notable 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, and as a reference for researchers. Differential equations. Functional analysis. Biomathematics. 70325 Population biology. 72060 Differential Equations. Functional Analysis. Mathematical and Computational Biology. 70327 Population Dynamics. 72062 Pang, Peter Y. H. author. aut http://id.loc.gov/vocabulary/relators/aut 75857 SpringerLink (Online service) Springer Nature eBook Printed edition: 9789819986910 Printed edition: 9789819986934 Printed edition: 9789819986941 https://doi.org/10.1007/978-981-99-8692-7 ZDB-2-SMA ZDB-2-SXMS 59433 59433