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Some Liouville Results for Quasilinear Hamilton-Jacobi Type Problems

Phuoc Vinh Dinh , Kim Anh T. Le , $icon-email$ Phuong Le

Abstract

We prove a Liouville type theorem for nonnegative solutions of the problem $- Δ_{p} u + | \nabla u |^{γ} = u^{q}$ in $R_{+}^{N}$ with zero Dirichlet boundary condition, where $p > 2$ and $q > γ > p - 1$ . Our proof combines a recent monotonicity result with a new Liouville type theorem for nonnegative stable solutions in dimension $N

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Some Liouville Results for Quasilinear Hamilton-Jacobi Type Problems

Abstract