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

作　　者：蒋玲芳[1] 何志乾[2] JIANG Lingfang;HE Zhiqian(Department of Mathematics,Leshan Vacationnal and Technical College,Leshan 614000,China;Department of Mathematics,Qianghai University,Xining 810016,China)

机构地区：[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

出　　处：《青海大学学报》2024年第1期100-106,共7页Journal of Qinghai University

基　　金：青海省自然科学基金项目(2021-ZJ-957Q);乐山市科技局项目(22ZRKX031)。

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-2)u'(t))'+λ(au-bu^(2)-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.The existence of multiple positive solutions of a steady-state reaction diffusion equation Neumann boundary value problem {|u'(t)|^(p-2)u'(t))'+λ(au-bu^(2)-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 diffusion coefficient.10,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/λ are 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 

分 类 号：O175.8[理学—数学]