一维p-Laplacian方程Neumann边值问题正解的存在性和多解性
Existence and multiplicity of positive solutions for Neumann boundary value problem of one-dimensional p-Laplacian equation
蒋玲芳 1何志乾2
作者信息
- 1. 乐山职业技术学院数学教研室,四川乐山 614000
- 2. 青海大学数理学院,青海西宁 810016
- 折叠
摘要
本文利用时间映像分析法考虑了 一类源自人口问题中的稳态反应扩散方程Neumann边值问题{(| u'(t)| p-2u'(t))'+λ(au-bu2-c)=0,0＜t＜1,u'(0)=u'(1)=0多个正解的存在性.其中,1/λ＞0为扩散系数,1＜p≤2,a＞0,b＞0,c＞0.进一步,当确定了 a,b,c,1/λ的值时,本文证明了上述问题多个正解的存在性和解的精确个数,所得结果推广并改进了已有文献的相关结果.
Abstract
The existence of multiple positive solutions of a steady-state reaction diffusion equation Neumann boundary value problem{(| u'(t)| p-2u'(t))'+λ(au-bu2-c)=0,0＜t＜1, u'(0)=u'(1)=0 derived from population problems is considered bythe time-map analysis method(1/λ＞0 is the dif-fusion coefficient.1＜p≤ 2,a＞0,b＞0,c＞0).Furthermore,the existence of multiple positive solutions and the exact number of solutions for the above problem are proved when the values of a,b,c,1/λare determined.The obtained results generalize and improve the relevant results of existing literatures.
关键词
人口模型/时间映像分析法/正解/多解Key words
population model/time-map analysis method/positive solution/multiplicity引用本文复制引用
基金项目
青海省自然科学基金(2021-ZJ-957Q)
乐山市科技局项目(22ZRKX031)
出版年
2024
NETL
NSTL
万方数据