TY - JOUR
T1 - Multiple solutions for a class of quasilinear problems with double criticality
AU - Ait-Mahiout, Karima
AU - Alves, Claudianor O.
AU - Garain, Prashanta
N1 - Publisher Copyright:
Copyright © The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.
PY - 2022/11/21
Y1 - 2022/11/21
N2 - We establish multiplicity results for the following class of quasilinear problems Pwhere for a generalized N-function. We consider to be a smooth bounded domain that contains two disjoint open regions and such that. The main feature of the problem is that the operator behaves like on and on. We assume the nonlinearity of two different types, but both behave like on and on as is large enough, for some 0$]]> and being the critical Sobolev exponent for <![CDATA[$1< p. In this context, for one type of nonlinearity, we provide a multiplicity of solutions in a general smooth bounded domain and for another type of nonlinearity, in an annular domain, we establish existence of multiple solutions for the problem that are non-radial and rotationally non-equivalent.
AB - We establish multiplicity results for the following class of quasilinear problems Pwhere for a generalized N-function. We consider to be a smooth bounded domain that contains two disjoint open regions and such that. The main feature of the problem is that the operator behaves like on and on. We assume the nonlinearity of two different types, but both behave like on and on as is large enough, for some 0$]]> and being the critical Sobolev exponent for <![CDATA[$1< p. In this context, for one type of nonlinearity, we provide a multiplicity of solutions in a general smooth bounded domain and for another type of nonlinearity, in an annular domain, we establish existence of multiple solutions for the problem that are non-radial and rotationally non-equivalent.
KW - Musielak-Sobolev space
KW - quasilinear problems
KW - variational methods
UR - http://www.scopus.com/inward/record.url?scp=85147507622&partnerID=8YFLogxK
U2 - 10.1017/S001309152200044X
DO - 10.1017/S001309152200044X
M3 - Article
AN - SCOPUS:85147507622
SN - 0013-0915
VL - 65
SP - 1011
EP - 1047
JO - Proceedings of the Edinburgh Mathematical Society
JF - Proceedings of the Edinburgh Mathematical Society
IS - 4
ER -