Singular Elliptic Problems: Bifurcation & Asymptotic Analysis

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Marius Ghergu (, Professor of Mathematics Romanian) Vicentiu Radulescu (, Professor of Mathematics Romanian)

Singular Elliptic Problems

Bifurcation & Asymptotic Analysis

Marius Ghergu (, Professor of Mathematics Romanian), Vicentiu Radulescu (, Professor of Mathematics Romanian)

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English

Oxford University Press Inc
29 May 2008

Calculus & mathematical analysis; Applied mathematics; Mathematical modelling; Non-linear science

Series: Oxford Lecture Series in Mathematics and Its Applications

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-Meinhardt systems 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 bifurcation problems. 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 asymptotic analysis, 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 with concrete 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

By: Marius Ghergu ( Professor of Mathematics Romanian), Vicentiu Radulescu (, Professor of Mathematics Romanian)
Imprint: Oxford University Press Inc
Country of Publication: United States
Dimensions: Height: 240mm, Width: 160mm, Spine: 20mm
Weight: 575g
ISBN: 9780195334722
ISBN 10: 0195334728
Series: Oxford Lecture Series in Mathematics and Its Applications
Pages: 320
Publication Date: 29 May 2008
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Hardback
Publisher's Status: Active

II BLOW-UP SOLUTIONS 2: Blow-up solutions for semilinear elliptic equations 3: Entire solutions blowing-up at infinity for elliptic systems III ELLIPTIC PROBLEMS WITH SINGULAR NONLINEARITIES 4: Sublinear perturbations of singular elliptic problems 5: Bifurcation and asymptotic analysis. The monotone case 6: Bifurcation and asymptotic analysis. The nonmonotone case 7: Superlinear perturbations of singular elliptic problems 8: Stability of the solution of a singular problem 9: The influence of a nonlinear convection term in singular elliptic problems 10: Singular Gierer-Meinhardt systems A Spectral theory for differential operators B Implicit function theorem C Ekeland's variational principle D Mountain pass theorem References Index

"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."