﻿ 广义Gray-Scott模型非常值正稳态解的不存在性 Nonexistence of Positive Nonconstant Stationary Solutions for Generalized Gray-Scott Model

Pure Mathematics
Vol.06 No.06(2016), Article ID:19037,6 pages
10.12677/PM.2016.66066

Nonexistence of Positive Nonconstant Stationary Solutions for Generalized Gray-Scott Model

Ling Yang, Ying Li

School of Science, Dalian Minzu University, Dalian Liaoning

Received: Nov. 3rd, 2016; accepted: Nov. 18th, 2016; published: Nov. 25th, 2016

ABSTRACT

In his paper, some sufficient conditions for nonexistence of positive nonconstant stationary solutions for generalized Gray-Scott model are given.

Keywords:Generalized Gray-Scott Model, Stationary Solution, Nonexistence

1. 引言

(1.1)

(i)

(ii)，则问题(1.1)不存在非常值正解。

(i)

(ii)

2. 定理1.1的证明

, ,

,

,

.

，依文献 [14] 中命题2.2，得

,

,

.

(2.1)

.

,

.

.

,

3. 定理1.2的证明

(3.1)

(3.2)

,

(3.3)

(3.4)

(3.5)

(3.6)

(3.7)

，于是由(3.7)可化为

Nonexistence of Positive Nonconstant Stationary Solutions for Generalized Gray-Scott Model[J]. 理论数学, 2016, 06(06): 480-485. http://dx.doi.org/10.12677/PM.2016.66066

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