Local behavior and global existence of positive solutions of auλ⩽−Δu⩽uλ
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We study the behavior near the origin of C2 positive solutions u(x) of auλ ≤ - Δu ≤ uλ in a punctured neighborhood of the origin in ℝn (n > 2) where the constants λ and a satisfy nn-2 < λ < n+2/n-2 and 0 < a < 1. We also study the existence of C2 positive solutions of (*) in ℝn. In both cases we show that changing a from one value in the open interval (0, 1) to another value in (0, 1) can have a dramatic effect. © 2002 Éditions scientifiques et médicales Elsevier SAS.
Annales de l'Institut Henri Poincaré C, Analyse non linéaire
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