Gradient estimates for ${\Delta }_{p}u-|\nabla u{|}^q+b(x)|u{|}^{r-1}u=0$ on a complete Riemannian manifold and Liouville type theorems

Dong Han, Jie He, Youde Wang

In this paper the Nash-Moser iteration method is used to study the gradient estimates of solutions to the quasilinear elliptic equation ${\Delta }_{p}u-|\nabla u{|}^q+b(x)|u{|}^{r-1}u=0$ define…