Positive solutions to superlinear second-order divergence type elliptic equations in cone-like domains
نویسندگان
چکیده
منابع مشابه
Positive solutions to superlinear second–order divergence type elliptic equations in cone–like domains
We study the problem of the existence and nonexistence of positive solutions to a superlinear second–order divergence type elliptic equation with measurable coefficients −∇ · a · ∇u = u (∗), p > 1, in an unbounded cone–like domain G ⊂ R (N ≥ 3). We prove that the critical exponent p∗(a,G) = inf{p > 1 : (∗) has a positive supersolution at infinity in G } for a nontrivial cone– like domain is alw...
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We study the existence and nonexistence of positive (super-) solutions to a singular semilinear elliptic equation −∇ · (|x|∇u)−B|x|u = C|x|u in cone–like domains of R (N ≥ 2), for the full range of parameters A,B, σ, p ∈ R and C > 0. We provide a complete characterization of the set of (p, σ) ∈ R such that the equation has no positive (super-) solutions, depending on the values of A,B and the p...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2005
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2004.03.003