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Quasilinear Elliptic Equations with Degenerations and Singularities.

By: Contributor(s): Material type: TextTextSeries: De Gruyter Series in Nonlinear Analysis and Applications SeriesPublisher: Berlin/Boston : Walter de Gruyter GmbH, 1997Copyright date: ©1997Edition: 1st edDescription: 1 online resource (232 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783110804775
Subject(s): Genre/Form: Additional physical formats: Print version:: Quasilinear Elliptic Equations with Degenerations and SingularitiesLOC classification:
  • QA377 -- .D76 1997eb
Online resources:
Contents:
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.
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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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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