Monotonicity of positive solutions to quasilinear elliptic equations in half-spaces with a changing-sign nonlinearity

Abstract

In this paper we prove the monotonicity of positive solutions to $-{\Delta }_{p}u=f(u)$ in half-spaces under zero Dirichlet boundary conditions, for $(2N+2)/(N+2)<p<2$ and for a general class of regular changing-sign nonlinearities $f$. The techniques used in the proof of the main result are based on a fine use of comparison and maximum principles and on an adaptation of the celebrated moving plane method to quasilinear elliptic equations in unbounded domains.

arXiv admin note: substantial text overlap with arXiv:2002.11970