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Multiple solutions for critical nonhomogeneous elliptic systems in noncontractible domain
Author(s) -
Duan Xueliang,
Wei Gongming,
Yang Haitao
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7289
Subject(s) - annulus (botany) , mathematics , bounded function , domain (mathematical analysis) , sobolev space , mathematical analysis , critical exponent , exponent , elliptic curve , pure mathematics , geometry , linguistics , philosophy , botany , scaling , biology
The paper is concerned with multiple solutions of a nonhomogeneous elliptic system with Sobolev critical exponent over a noncontractible domain, precisely, a smooth bounded annular domain. We prove the existence of four solutions using variational methods and Lusternik–Schnirelmann theory, when the inner hole of the annulus is sufficiently small.