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

被引：29

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

共 50 条

[21] Monotonicity and one-dimensional symmetry for solutions of −Δpu = f(u) in half-spaces
Alberto Farina
Luigi Montoro
Berardino Sciunzi
Calculus of Variations and Partial Differential Equations, 2012, 43 : 123 - 145
[22] EXISTENCE OF SOLUTIONS IN WEIGHTED SOBOLEV SPACES FOR SOME DEGENERATE QUASILINEAR ELLIPTIC EQUATIONS
Cavalheiro, Albo Carlos
GEORGIAN MATHEMATICAL JOURNAL, 2008, 15 (04) : 627 - 634
[23] Existence of Solutions for Some Quasilinear Degenerate Elliptic Inclusions in Weighted Sobolev Spaces
Cheng, Yi
Li, Cuiying
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2016, 37 (01) : 40 - 50
[24] A strongly degenerate quasilinear equation:: the elliptic case
Andreu, F
Caselles, V
Mazón, JM
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2004, 3 (03) : 555 - 587
[25] Quasilinear degenerate elliptic equation with absorption term
Horiuchi, T
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 47 (03) : 1649 - 1657
[26] EIGENVALUE PROBLEMS OF A DEGENERATE QUASILINEAR ELLIPTIC EQUATION
Pao, C. V.
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2010, 40 (01) : 305 - 311
[27] Existence of solutions for a class of degenerate quasilinear elliptic equation in RN with vanishing potentials
Waldemar D Bastos
Olimpio H Miyagaki
Rônei S Vieira
Boundary Value Problems, 2013
[28] Existence of solutions for a class of degenerate quasilinear elliptic equation in RN with vanishing potentials
Bastos, Waldemar D.
Miyagaki, Olimpio H.
Vieira, Ronei S.
BOUNDARY VALUE PROBLEMS, 2013,
[29] Existence of solutions for quasilinear degenerate elliptic equations
Akdim, Y.
Azroul, E.
Benkirane, A.
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2001,
[30] Existence of solutions for degenerate quasilinear elliptic equations
Zou, Weilin
Li, Fengquan
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (09) : 3069 - 3082

← 1 2 3 4 5 →