Release Time:2019-03-11  Hits:

Indexed by: Journal Article

Date of Publication: 2017-10-01

Journal: ACTA MATHEMATICA SINICA-ENGLISH SERIES

Included Journals: SCIE、Scopus

Volume: 33

Issue: 10

Page Number: 1382-1396

ISSN: 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.