Some Remarks on Liouville Type Results For Quasilinear Elliptic Equations

Yihong Du; Edward Norman Dancer

Some Remarks on Liouville Type Results For Quasilinear Elliptic Equations

Yihong Du, Edward Norman Dancer

Research output: Contribution to journal › Article › peer-review

27 Citations (Scopus)

Abstract

For a wide class of nonlinearities f(u) satisfying f(0)=f(a)=0, f(u)>0 in (0,a) and f(u)<0 in (a,∞), we show that any nonnegative solution of the quasilinear equation -Δpu=f(u) over the entire ℝ^N must be a constant. Our results improve or complement some recently obtained Liouville type theorems. In particular, we completely answer a question left open by Du and Guo.

Original language	English
Pages (from-to)	1891-1899
Journal	Proceedings of the American Mathematical Society
Volume	131
Issue number	6
Publication status	Published - 2003

Keywords

Ordinary Differential Equations, Difference Equations and Dynamical Systems

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title = "Some Remarks on Liouville Type Results For Quasilinear Elliptic Equations",

abstract = "For a wide class of nonlinearities f(u) satisfying f(0)=f(a)=0, f(u)>0 in (0,a) and f(u)<0 in (a,∞), we show that any nonnegative solution of the quasilinear equation -Δpu=f(u) over the entire ℝ\textasciicircum{}N must be a constant. Our results improve or complement some recently obtained Liouville type theorems. In particular, we completely answer a question left open by Du and Guo.",

keywords = "Ordinary Differential Equations, Difference Equations and Dynamical Systems",

author = "Yihong Du and Dancer, \{Edward Norman\}",

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N2 - For a wide class of nonlinearities f(u) satisfying f(0)=f(a)=0, f(u)>0 in (0,a) and f(u)<0 in (a,∞), we show that any nonnegative solution of the quasilinear equation -Δpu=f(u) over the entire ℝ^N must be a constant. Our results improve or complement some recently obtained Liouville type theorems. In particular, we completely answer a question left open by Du and Guo.

AB - For a wide class of nonlinearities f(u) satisfying f(0)=f(a)=0, f(u)>0 in (0,a) and f(u)<0 in (a,∞), we show that any nonnegative solution of the quasilinear equation -Δpu=f(u) over the entire ℝ^N must be a constant. Our results improve or complement some recently obtained Liouville type theorems. In particular, we completely answer a question left open by Du and Guo.

KW - Ordinary Differential Equations, Difference Equations and Dynamical Systems

UR - http://www.jstor.org/stable/info/1194368

UR - https://www.scopus.com/pages/publications/0038062729

M3 - Article

SN - 0002-9939

VL - 131

SP - 1891

EP - 1899

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 6

ER -

Some Remarks on Liouville Type Results For Quasilinear Elliptic Equations

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