Quasilinear elliptic equations with degenerations and singularities /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Drábek, Pavel, 1953-
Otros Autores: Kufner, Alois, Nicolosi, Francesco, 1938-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin ; New York : W. de Gruyter, 1997.
Colección:De Gruyter series in nonlinear analysis and applications ; 5.
Temas:
Differential equations, Elliptic > Numerical solutions.
Boundary value problems > Numerical solutions.
Bifurcation theory.
Équations différentielles elliptiques > Solutions numériques.
Problèmes aux limites > Solutions numériques.
Théorie de la bifurcation.
MATHEMATICS > Differential Equations > Partial.
Bifurcation theory
Boundary value problems > Numerical solutions
Differential equations, Elliptic > Numerical solutions
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 lemmas2 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 notation3.2 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 â??N
  • 4.1 Nonlinear eigenvalue problem
  • 4.2 Bifurcation problem for the p-Laplacian in â??N
  • 4.3 Bifurcation problem for the perturbed p-Laplacian in â??N
  • Bibliography
  • Index

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