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Author Kufner, Alois
Title Quasilinear Elliptic Equations with Degenerations and Singularities
Imprint Berlin/Boston : De Gruyter, Inc., 1997
book jacket
Descript 1 online resource (231 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series De Gruyter Series in Nonlinear Analysis and Applications Ser. ; v.5
De Gruyter Series in Nonlinear Analysis and Applications Ser
Note Intro -- List of symbols, theorems, definitions, assumptions, examples -- List of symbols -- List of theorems -- List of definitions -- List of assumptions -- List of examples -- 0 Introduction -- 1 Preliminaries -- 1.1 The domain Ω -- 1.2 Function spaces -- 1.3 Caratheodory functions, Nemytskij (superposition) operators -- 1.4 Function spaces (continued) -- 1.5 Weighted Sobolev spaces -- 1.6 Leray-Lions theorem -- 1.7 Degree of mappings of monotone type -- 1.8 Harnack-type inequality, decay of solution, local regularity and interpolation inequality -- 1.9 Some technical lemmas -- 2 Solvability of nonlinear boundary value problems -- 2.1 Formulation of the problem -- 2.2 Second order equations (bounded domains) -- 2.3 Second order equations (proof of Theorem 2.1) -- 2.4 Second order equations (unbounded domains) -- 2.5 Higher order equations (growth conditions) -- 2.6 Higher order equations (operator representation) -- 2.7 Higher order equations (degree of the mapping T) -- 2.8 Higher order equations (existence results) -- 2.9 Examples, remarks, comments -- 3 The degenerated p-Laplacian on a bounded domain -- 3.1 Basic notation -- 3.2 Existence of the least eigenvalue of the homogeneous eigenvalue problem -- 3.3 Existence of the least eigenvalue of the nonhomogeneous eigenvalue problem -- 3.4 Maximum principle for degenerated (singular) equations -- 3.5 Positive solutions of degenerated (singular) BVP -- 3.6 Bifurcation from the least eigenvalue -- 4 The p-Laplacian in ℝN -- 4.1 Nonlinear eigenvalue problem -- 4.2 Bifurcation problem for the p-Laplacian in ℝN -- 4.3 Bifurcation problem for the perturbed p-Laplacian in ℝN -- Bibliography -- Index
The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Please submit book proposals toJürgen Appell
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Kufner, Alois Quasilinear Elliptic Equations with Degenerations and Singularities Berlin/Boston : De Gruyter, Inc.,c1997 9783110154900
Subject Differential equations, Elliptic -- Numerical solutions.;Boundary value problems -- Numerical solutions.;Bifurcation theory
Electronic books
Alt Author Nicolosi, Francesco
ábek, Pavel
Nicolosi, Francesco
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