This article is cited in 1 paper

On monotonicity of solutions of Dirichlet problem for some quasilinear elliptic equations in half-spaces

O. A. Salieva

Department of Applied Mathematics, Moscow State Technological University “Stankin”, 3a Vadkovsky pereulok, 127993 Moscow, Russia

Abstract: We prove the monotonicity of nonnegative bounded solutions to the Dirichlet problem for a quasilinear elliptic equation of the form $-\Delta_p u=f(u)g(x_n)$ with $p\geqslant3$ in a half-space, where $x_n$ is the normal coordinate of the argument. This assertion implies new nonexistence results for the case $f(u)=u^q$ with the appropriate values of $q$.

Keywords and phrases: quasilinear equations, monotonicity, nonexistence of solutions.

MSC: 35J60, 35J70, 35J92

Received: 14.10.2015

Language: English

Bibliographic databases:

•