Multiplicity of positive solutions for quasilinear elliptic problems involving the p -Laplacian operator

In this work, we establish the existence and multiplicity of positive solutions for an elliptic problem involving the p-Laplacian operator with subcritical growth in RN. More specifically, we consider the nonlocal elliptic problem: {−Δpu+V(x)|u|p−2u=−μg(x)|u|r−2u+λf(x)|u|q−2uinRN,u∈W1,p(RN), where μ,λ>0 and p 0 is the largest positive value where the Nehari method can be applied directly. Recall that there exist inflection points for the associated fibering map for our main problem. Furthermore, we prove a regularity result using the Moser iteration, which allows us to prove that any nonzero and nonnegative solution to our main problem is strictly positive.