In this paper we prove the monotonicity of positive solutions to $-\Delta_pu = f(u) $ in half-spaces under zero Dirichlet boundary conditions, for$(2N+2)/(N+2) < p < 2$ and for a general class of regular sign-changing 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 adaptationof the celebrated moving plane method to quasilinear elliptic equations in unbounded domains.

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

Francesco Esposito;Luigi Montoro;Berardino Sciunzi
2022

Abstract

In this paper we prove the monotonicity of positive solutions to $-\Delta_pu = f(u) $ in half-spaces under zero Dirichlet boundary conditions, for$(2N+2)/(N+2) < p < 2$ and for a general class of regular sign-changing 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 adaptationof the celebrated moving plane method to quasilinear elliptic equations in unbounded domains.
Mathematics - Analysis of PDEs
Mathematics - Analysis of PDEs
35J62, 35J92, 35B06, 35B50, 35B51
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/327429
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