Singular Elliptic Problems: Bifurcation and Asymptotic Analysis

Hardcover | April 8, 2008

byMarius Ghergu, Vicentiu Radulescu

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This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by singular elliptic equations. There are carefully analyzed logistic type equations with boundary blow-up solutions and generalized Lane-Emden-Fowler equations or Gierer-Meinhardtsystems with singular nonlinearity in anisotropic media. These nonlinear problems appear as mathematical models in various branches of Physics, Mechanics, Genetics, Economics, Engineering, and they are also relevant in Quantum Physics and Differential Geometry. One of the main purposes of this volume is to deduce decay rates for general classes of solutions in terms of estimates of particular problems. Much of the material included in this volume is devoted to the asymptotic analysis of solutions and to the qualitative study of related bifurcationproblems. Numerical approximations illustrate many abstract results of this volume. A systematic description of the most relevant singular phenomena described in these lecture notes includes existence (or nonexistence) of solutions, unicity or multiplicity properties, bifurcation and asymptoticanalysis, and optimal regularity. The method of presentation should appeal to readers with different backgrounds in functional analysis and nonlinear partial differential equations. All chapters include detailed heuristic arguments providing thorough motivation of the study developed later on in the text, in relationship withconcrete processes arising in applied sciences. The book includes an extensive bibliography and a rich index, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of nonlinear singular phenomena

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This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by singular elliptic equations. There are carefully analyzed logistic type equations with boundary blow-up solutions and generalized Lane-Emden-Fowler equations or Gierer-Meinhardtsystems with singular nonlinearity in anisotropic ...

Marius Ghergu is Researcher at the Institute of Mathematics "Simion Stoilow" of the Romanian Academy. Vicentiu Radulescu is Senior Researcher at the Institute of Mathematics "Simion Stoilow" of the Romanian Academy and Full Professor at the University of Craiova.

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Format:HardcoverDimensions:320 pages, 6.3 × 9.29 × 0.79 inPublished:April 8, 2008Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0195334728

ISBN - 13:9780195334722

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Table of Contents

II BLOW-UP SOLUTIONS2. Blow-up solutions for semilinear elliptic equations3. Entire solutions blowing-up at infinity for elliptic systemsIII ELLIPTIC PROBLEMS WITH SINGULAR NONLINEARITIES4. Sublinear perturbations of singular elliptic problems5. Bifurcation and asymptotic analysis. The monotone case6. Bifurcation and asymptotic analysis. The nonmonotone case7. Superlinear perturbations of singular elliptic problems8. Stability of the solution of a singular problem9. The influence of a nonlinear convection term in singular elliptic problems10. Singular Gierer-Meinhardt systemsA Spectral theory for differential operatorsB Implicit function theoremC Ekeland's variational principleD Mountain pass theoremReferencesIndex