Quasi-linear equation $\hat{I}{”}_{p}v+a{v}^q=0$ on manifolds with integral bounded Ricci curvature and geometric applications

Youde Wang, Guodong Wei, Liqin Zhang

We study nonexistence results and gradient estimates for solutions of \[ Δ_p v + a v^{q}=0 \] defined on complete Riemannian manifolds satisfying a \emph{$\ddot{I}‡$-type Sobolev inequal…