Positive solutions for a class semipositone quasilinear problem with Orlicz–Sobolev critical growth

This is the authors' abstract. We don't add key points for this paper.

In this work, we study the existence of positive solutions for the following class of semipositone quasilinear problems: where is a bounded domain, , are parameters, is a Caractheodory function, and has a critical growth with relation to the Orlicz–Sobolev space . The main tools used are variational methods, a concentration compactness theorem for Orlicz–Sobolev space and some priori estimates.