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Some Liouville Results for Quasilinear Hamilton-Jacobi Type Problems
Phuoc Vinh Dinh
,
Kim Anh T. Le
,
Phuong Le
Abstract
We prove a Liouville type theorem for nonnegative solutions of the problem $-\Delta_p u + |\nabla u|^\gamma = u^q$ in $\mathbb {R}^N_+$ with zero Dirichlet boundary condition, where $p>2$ and $q>\gamma > p-1$. Our proof combines a recent monotonicity result with a new Liouville type theorem for nonnegative stable solutions in dimension $N