The maximum principle with lack of monotonicity

Abstract

We establish a maximum principle for the weighted $(p,q)$-Laplacian, which extends the general Pucci–Serrin strong maximum principle to this quasilinear abstract setting. The feature of our main result is that it does not require any monotonicity assumption on the nonlinearity. The proof combines a local analysis with techniques on nonlinear differential equations.

Keywords

• generalized maximum principle
• $(p
• q)$-operator
• nonlinear differential inequality
• normal derivative
• positive solution