Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations

  • Messoud Efendiev

Part of the Fields Institute Monographs book series (FIM, volume 36)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Messoud Efendiev
    Pages 1-70
  3. Messoud Efendiev
    Pages 163-175
  4. Messoud Efendiev
    Pages 177-186
  5. Messoud Efendiev
    Pages 187-198
  6. Messoud Efendiev
    Pages 199-224
  7. Messoud Efendiev
    Pages 225-252
  8. Back Matter
    Pages 253-258

About this book


This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.


Sobolev spaces Nemytskii operator trajectory attractor Laplace operator symmetry and attractors stabilization properties reduction of dynamics

Authors and affiliations

  • Messoud Efendiev
    • 1
  1. 1.Institute of Computational BiologyHelmholtz Center MunichNeuherbergGermany

Bibliographic information