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arXiv · 2112.09552

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

Francesco Esposito·Alberto Farina·Luigi Montoro·Berardino Sciunzi
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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.

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Francesco Esposito, Alberto Farina, Luigi Montoro, Berardino Sciunzi. 2021-12-16. Monotonicity of positive solutions to quasilinear elliptic equations in half-spaces with a changing-sign nonlinearity. https://arxiv.org/abs/2112.09552

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