A CRITICAL PHENOMENON FOR SUBLINEAR ELLIPTIC EQUATIONS IN CONE-LIKE DOMAINS
نویسندگان
چکیده
منابع مشابه
A critical phenomenon for sublinear elliptic equations in cone–like domains
We study positive supersolutions to an elliptic equation (∗) −∆u = c|x|u, p, s ∈ R, in cone–like domains in R (N ≥ 2). We prove that in the sublinear case p < 1 there exists a critical exponent p∗ < 1 such that equation (∗) has a positive supersolution if and only if −∞ < p < p∗. The value of p∗ is determined explicitly by s and the geometry of the cone.
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In this paper, a priori estimates of positive solutions for sublinear elliptic equations are given in terms of thicknesses of domains. To this end, a supersolution is constructed by a composite function of a solution to an ordinary differential equation and a distance function. The results work efficiently in the case where the domain is an exterior or an interior of a convex set.
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2005
ISSN: 0024-6093,1469-2120
DOI: 10.1112/s0024609305004492