Quasilinear elliptic equations involving the NN-Laplacian with critical exponential growth in RNRN

This paper shows the existence of nontrivial solutions for the quasilinear equations of the form −ΔNu+V(x)|u|N−2u−ΔN(u2)u=h(u)in RN, where ΔNΔN is the NN-Laplacian operator, VV is a continuous function bounded from below away from zero and h(u)h(u) is a continuous function having critical exponential growth.