TY - JOUR
T1 - Multiplicity of positive solutions for a nonlinear equation with a Hardy potential on the Heisenberg group
AU - Kassymov, Aidyn
AU - Suragan, Durvudkhan
N1 - Funding Information:
This research was funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP08855571 ). This work was also supported in parts by the Nazarbayev University program 091019CRP2120 .
Publisher Copyright:
© 2020 Elsevier Masson SAS
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/12
Y1 - 2020/12
N2 - In this note, we show multiplicity of positive weak solutions for nonlinear equations with a first stratum Hardy potential on the Heisenberg and stratified groups. The mountain pass theorem, Sobolev-Folland-Stein and first stratum Hardy inequalities play key roles in our proofs.
AB - In this note, we show multiplicity of positive weak solutions for nonlinear equations with a first stratum Hardy potential on the Heisenberg and stratified groups. The mountain pass theorem, Sobolev-Folland-Stein and first stratum Hardy inequalities play key roles in our proofs.
KW - Hardy inequality
KW - Heisenberg group
KW - Mountain pass theorem
KW - Sobolev-Folland-Stein inequality
KW - Stratified group
KW - Sub-Laplacian
UR - https://www.scopus.com/pages/publications/85093670246
UR - https://www.scopus.com/inward/citedby.url?scp=85093670246&partnerID=8YFLogxK
U2 - 10.1016/j.bulsci.2020.102916
DO - 10.1016/j.bulsci.2020.102916
M3 - Article
AN - SCOPUS:85093670246
SN - 0007-4497
VL - 165
JO - Bulletin des Sciences Mathematiques
JF - Bulletin des Sciences Mathematiques
M1 - 102916
ER -