Entire solutions of quasilinear elliptic equations

We consider the existence of entire solutions of a quasilinear elliptic equation div(|Du|p−2Du)=k(x)f(u),x∈RN, where p>1p>1, N∈NN∈N. Conditions of the existence of entire solutions have been obtained by different authors. We prove an optimality of some of these results and give new sufficient conditions for the nonexistence of entire solutions.