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Indexed by:期刊论文
Date of Publication:2017-10-01
Journal:ACTA MATHEMATICA SINICA-ENGLISH SERIES
Included Journals:Scopus、SCIE
Volume:33
Issue:10
Page Number:1382-1396
ISSN No.:1439-8516
Key Words:Pohozaev identity; fractional Laplacian; Henon system; nonexistence of solutions
Abstract:In this paper, we study the Pohozaev identity associated with a Henon-Lane-Emden system involving the fractional Laplacian:
{(-Delta)(s)u = vertical bar x vertical bar(a)v(p), x is an element of Omega,
(-Delta)(S)v = vertical bar x vertical bar(b)u(q), x is an element of Omega,
u = v = 0, x is an element of R-n\Omega,
in a star-shaped and bounded domain Omega for s is an element of(0, 1). As an application of our identity, we deduce the nonexistence of positive solutions in the critical and supercritical cases.