Journal of Fixed Point Theory and Applications

, Volume 19, Issue 1, pp 205–213

On the behavior of positive solutions of semilinear elliptic equations in asymptotically cylindrical domains


DOI: 10.1007/s11784-016-0349-1

Cite this article as:
Chipot, M., Dávila, J. & del Pino, M. J. Fixed Point Theory Appl. (2017) 19: 205. doi:10.1007/s11784-016-0349-1


The goal of this note is to study the asymptotic behavior of positive solutions for a class of semilinear elliptic equations which can be realized as minimizers of their energy functionals. This class includes the Fisher-KPP and Allen–Cahn nonlinearities. We consider the asymptotic behavior in domains becoming infinite in some directions. We are in particular able to establish an exponential rate of convergence for this kind of problems.


Semilinear elliptic equation Cylindrical domain Asymptotic behavior 

Mathematics Subject Classification

35J15 35J25 35J61 

Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Institute of Applied MathematicsUniversity of ZürichZürichSwitzerland
  2. 2.Departamento de Ingenierıa Matemática and Centro de Modelamiento MatemáticoUniversidad de ChileSantiagoChile

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