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Liouville theorems for nonlinear elliptic equations with gradient dependence in half-spaces Sirakov, Boyan


We study the existence of nonnegative supersolutions of the nonlinear elliptic problem $-\Delta u + |\nabla u|^q = \lambda u^p$ in the half-space $\R^N_+$, where $N\ge 2$, $q>1$, $p>0$ and $\la>0$. We obtain Liouville theorems for positive, bounded supersolutions, depending on the exponents $q$ and $p$, the dimension $N$, and, in some critical cases, also on the parameter $\la>0$.

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