论文摘要
本文首先讨论分数阶Laplacian算子齐次混合边界特征值问题其中0<s<1,Ω是Rd（d>2s）中的有界的C1,1区域,B是齐次混合边界条件.当a和b∈L∞（Ω）,且inf b（xr）≥δ>0时.得到主特征值λ1Ω[α,B]和趋于无穷大的特征值序列的存在性,研究了主特征值λ1Ω[a,B]对权函数a和区域Ω的连续依赖性,并通过Moser型迭代对主特征函数u1叫进行正则性估计得u1∈Cγ（Ω）（γ ∈（0,1））,同时给出与主特征值相关的一些不等式.其次,作为对主特征问题的应用,考虑齐次混合边界Logistic型问题这里h（x,u）满足一定的假设.通过构造拟单调算子,利用上下解方法得到上述问题存在正解u∈L∞（Ω）当且仅当主特征值λ1Ω[a-λ,B]<0.所得结果是对Cano-Casanova等人[JDE2002]、Fraile等人[JDE1996]和Lopez-Gomez[JDE1996]中部分结论的非局部推广.
论文目录
文章来源
类型: 硕士论文
作者: 路金娇
导师: 孙红蕊
关键词: 特征值问题,分数阶,混合边界
来源: 兰州大学
年度: 2019
分类: 基础科学
专业: 数学
单位: 兰州大学
分类号: O175
总页数: 43
文件大小: 1482K
下载量: 30
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