Multiple solutions for a class of quasilinear problems with double criticality

Abstract

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. Copyright © The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.