Solutions of a weighted \(p\)-Laplacian critical Sobolev problem (Q2306205)

This paper is concerned with the study of combined effects of a subcritical power-type nonlinearity and a critical reaction in the abstract seeting of a quasilinear Dirichlet problem. The authors are interested in the existence of positive solutions. This is done in accordance with the growth of a related potential near its minima and the position of the subcritical exponent with respect to the dimension of the space. The proofs combine analytical and variational methods.