Fading absorption in non-linear elliptic equations

Moshe Marcus, Andrey Shishkov

We study the equation $-\Delta u+h(x)|u{|}^{q-1}u=0$, $q>1$, in $R^N_+=R^{N-1}\ti R_+$ where $h\in C(\overline{R_{+}^N})$, $h\ge 0$. Let $(x_1,...,x_N)$ be a coordinate system such that $R^N_+=…