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Titlebook: An Introduction to Nonlinear Functional Analysis and Elliptic Problems; Antonio Ambrosetti,David Arcoya Textbook 2011 Springer Science+Bus

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期刊全稱An Introduction to Nonlinear Functional Analysis and Elliptic Problems
影響因子2023Antonio Ambrosetti,David Arcoya
視頻videohttp://file.papertrans.cn/156/155396/155396.mp4
發(fā)行地址Provides the basic, abstract tools used in nonlinear analysis.Key results such as the Banach contraction principle, a fixed point theorem for increasing operators, local and global inversion theory, L
學(xué)科分類Progress in Nonlinear Differential Equations and Their Applications
圖書封面Titlebook: An Introduction to Nonlinear Functional Analysis and Elliptic Problems;  Antonio Ambrosetti,David Arcoya Textbook 2011 Springer Science+Bus
影響因子.This self-contained textbook provides the basic, abstract?tools?used in?nonlinear analysis?and their applications to semilinear elliptic boundary value problems.?By first?outlining the advantages and disadvantages of each method, this comprehensive text?displays how various?approaches?can easily be?applied?to a range of model cases..An Introduction to Nonlinear Functional Analysis and Elliptic Problems.?is divided into two parts: the first discusses key?results such as the Banach contraction principle, a fixed point theorem for increasing operators, local and global inversion theory, Leray–Schauder degree, critical point theory, and bifurcation theory; the second part shows how these abstract results apply to Dirichlet elliptic boundary value problems. The exposition is driven by numerous prototype problems and exposes a variety of approaches to?solving them..Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is a?practical text for an introductory course or seminar on nonlinear functional analysis..
Pindex Textbook 2011
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Superlinear Problems,s case an appropriate approach seems to be critical point theory. Actually, the mountain pass theorem or the linking theorem can be used to find solutions. We also show how to study superlinear problems by using the topological degree.
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Quasilinear Problems,ed because the Euler functional fails to be .. This critical point result is discussed in Section 12.2 and is applied to boundary value problems in Section 12.3. A nonvariational equation is also considered in Section 12.4, where we apply the global bifurcation theorem (see Theorem 4.4.1).
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https://doi.org/10.1007/978-0-8176-8114-2Leray--Schauder topological degree; bifurcation theory; critical points; elliptic problems; fixed point
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