Applied Mathematics and Optimization

, Volume 12, Issue 1, pp 271–282

Semilinear equations in ℝN without condition at infinity

  • H. Brezis

DOI: 10.1007/BF01449045

Cite this article as:
Brezis, H. Appl Math Optim (1984) 12: 271. doi:10.1007/BF01449045


In this paper we establish that some nonlinear elliptic (and parabolic) problems are well posed in all of ℝN without prescribing the behavior at infinity. A typical example is the following: Let 1<p<∞. For everyf ∈ Lloc1(ℝN) there is a uniqueu ∈ Llocp(ℝN) satisfying
$$ - \Delta u + |u|^{p - 1} u = f(x) on \mathbb{R}^N $$

Copyright information

© Springer-Verlag New York Inc. 1984

Authors and Affiliations

  • H. Brezis
    • 1
  1. 1.Université Paris VIParis Cedex 05France