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A Critical Phenomenon for Sublinear Elliptic Equations in Cone-Like Domains |
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| Authors: | Kondratiev Vladimir; Liskevich Vitali; Moroz Vitaly; Sobol Zeev |
| Institution: | Department of Mathematics and Mechanics, Moscow State University Moscow 119 899, Russia kondrat{at}vnmok.math.msu.su School of Mathematics, University of Bristol Bristol BS8 1TW, United Kingdom v.liskevich{at}bristol.ac.uk, v.moroz{at}bristol.ac.uk Department of Mathematics, University of Wales Swansea Singleton Park, Swansea SA2 8PP, United Kingdom z.sobol{at}swansea.ac.uk |
| Abstract: | The authors of this paper study positive supersolutions to theelliptic equation - u = c|x|–sup in Cone-like domains ofRN (N  2), where p, s  R and c > 0. They prove that in thesublinear case p < 1 there exists a critical exponent p*> 1 such that the equation has a positive supersolution ifand only if – < p < p*. The value of p* is determinedexplicitly by s and the geometry of the cone. 2000 MathematicsSubject Classification 35J60 (primary), 35B05, 35R45 (secondary). |
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