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

Francesco Esposito (1, 2) , Alberto Farina (2) , Luigi Montoro , Berardino Sciunzi (3)

1 SZN - Stazione Zoologica Anton Dohrn
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
3 Dipartimento di Matematica

In this paper we prove themonotonicity 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.

Domaines: Mathématiques [math]

Francesco Esposito, Alberto Farina, Luigi Montoro, Berardino Sciunzi. Monotonicity of positive solutions to quasilinear elliptic equations in half-spaces with a changing-sign nonlinearity. Calculus of Variations and Partial Differential Equations, 2022, 61 (4), ⟨10.1007/s00526-022-02250-3⟩. ⟨hal-03712135⟩