Semilinear equations in ℝ N without condition at infinity
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Abstract
In this paper we establish that some nonlinear elliptic (and parabolic) problems are well posed in all of ℝ N without prescribing the behavior at infinity. A typical example is the following: Let 1<p<∞. For everyf ∈ L loc 1 (ℝ N ) there is a uniqueu ∈ L loc p (ℝ N ) satisfying.
$$ - \Delta u + |u|^{p - 1} u = f(x) on \mathbb{R}^N $$
Keywords
System Theory Mathematical Method
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© Springer-Verlag New York Inc. 1984