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Monotonicity results in half-spaces for the p-Laplacian

Published online by Cambridge University Press:  03 June 2015

Berardino Sciunzi
Berardino Sciunzi*
Affiliation:
Dipartimento di Matematica, Università della Calabria, Ponte Pietro Bucci 31B, 87036 Arcavacata di Rende, Cosenza, Italy, (sciunzi@mat.unical.it)
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Abstract

We prove monotonicity properties of positive weak solutions to – Δpu = f(u) in half-spaces for the case in which (2N + 2)/(N + 2) < p < 2 when zero Dirichlet boundary conditions are imposed. The model nonlinearity is given by f(s) := sq − λsm with q > m ≥ p − 1 and λ > 0.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 3 , June 2015 , pp. 597 - 610
Copyright
Copyright © Royal Society of Edinburgh 2015 

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