Archive for Rational Mechanics and Analysis

, Volume 106, Issue 3, pp 217–241

Elliptic and parabolic semilinear problems without conditions at infinity

  • Francisco Bernis

DOI: 10.1007/BF00281214

Cite this article as:
Bernis, F. Arch. Rational Mech. Anal. (1989) 106: 217. doi:10.1007/BF00281214


I prove that some semilinear elliptic and parabolic problems of arbitrary even order are well-posed in all of ℝN without conditions at infinity. In particular, the growth of the data at infinity need not be limited and the solution is unique without prescription of its behavior at infinity. This is partly a higher-order generalization of the results obtained by Brezis (Appl. Math. Optim. 12, (1984), 271–282) for second-order problems.

Copyright information

© Springer-Verlag GmbH & Co 1989

Authors and Affiliations

  • Francisco Bernis
    • 1
  1. 1.Departamento de Matematica AplicadaUniversidad Complutense de MadridSpain

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