Nonlinear Second Order Elliptic Equations

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 solu...

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Huvudupphovsmän: Wang, Mingxin (Författare, medförfattare), Pang, Peter Y. H. (Författare, medförfattare)
Institutionell upphovsman: SpringerLink (Online service)
Materialtyp: Elektronisk E-bok
Språk:engelska
Publicerad: Singapore : Springer Nature Singapore : Imprint: Springer, 2024.
Upplaga:1st ed. 2024.
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Länkar:https://doi.org/10.1007/978-981-99-8692-7
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505 0 |a 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. 
520 |a 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. 
532 8 |a Accessibility summary: This PDF does not fully comply with PDF/UA standards, but does feature limited screen reader support, bookmarks for easy navigation and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com. 
532 8 |a No reading system accessibility options actively disabled 
532 8 |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com 
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