Compact Sobolev embeddings and positive solutions to a quasilinear equation with mixed nonlinearities.

In this paper, we study the existence and multiplicity results of nontrivial positive solutions to the following quasilinear elliptic equation on R N , when N ≥ 2 , − Δ p u = λ K (x) u r − 1 − V (x) u q − 1. Here, K (x) , V (x) > 0 are suitable potentials, 1 < p < r < q < ∞ , and λ > 0 is a parameter. To study this problem, some compact embedding results regarding M V q , p (R N) ↪ L K r (R N) are proved that unify and extend some recent results of the author [12–14]. [ABSTRACT FROM AUTHOR]