Abstract
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 ∈ L 1loc (ℝN) there is a uniqueu ∈ L ploc (ℝN) satisfying
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Communicated by D. Kinderlehrer
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Brezis, H. Semilinear equations in ℝN without condition at infinity. Appl Math Optim 12, 271–282 (1984). https://doi.org/10.1007/BF01449045
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DOI: https://doi.org/10.1007/BF01449045