Applied Mathematics and Optimization

, Volume 12, Issue 1, pp 271–282 | Cite as

Semilinear equations in ℝN without condition at infinity

  • H. Brezis


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
$$ - \Delta u + |u|^{p - 1} u = f(x) on \mathbb{R}^N $$


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Copyright information

© Springer-Verlag New York Inc. 1984

Authors and Affiliations

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

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