Monotonicity of solutions of quasilinear degenerate elliptic equation in half-spaces

被引：32

作者：

Farina, Alberto ^{[1
]}

Montoro, Luigi ^{[2
]}

Sciunzi, Berardino ^{[2
]}

机构：

[1] Univ Picardie Jules Verne, LAMFA, CNRS, UMR 6140, Amiens, CT, France

[2] Univ Calabria, Dipartimento Matemat, I-87036 Cosenza, CT, Italy

来源：

MATHEMATISCHE ANNALEN | 2013年 / 357卷 / 03期

关键词：

POSITIVE SOLUTIONS; UNBOUNDED-DOMAINS; REGULARITY; MAXIMUM; SYMMETRY; NONEXISTENCE; INEQUALITIES; LIOUVILLE; EXISTENCE;

D O I：

10.1007/s00208-013-0919-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a weak comparison principle in narrow unbounded domains for solutions to in the case and is a power-type nonlinearity, or in the case and is super-linear. We exploit it to prove the monotonicity of positive solutions to in half spaces (with zero Dirichlet assumption) and therefore to prove some Liouville-type theorems.

引用

页码：855 / 893

页数：39

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