Existence of solutions for a class of quasilinear elliptic equations involving the <i>p</i>-Laplacian

This paper is concerned with the existence of solutions for quasilinear elliptic equations −Δpu−Δp(|u|2α)|u|2α−2u+V(x)|u|p−2u=|u|q−2u,x∈RN, where α≥1, 10 a continuous function. In this work, we mainly focus on nontrivial solutions. When 2αp<q<p∗, establish by using Mountain-Pass lemma; when q≥2αp∗, Pohozaev type variational identity, prove that equation has no