The spectral analysis for a singular fractional differential equation with a signed measure

被引：93

作者：

Zhang, Xinguang ^{[1
,3
]}

Liu, Lishan ^{[2
,3
]}

Wu, Yonghong ^{[3
]}

Wiwatanapataphee, B. ^{[3
]}

机构：

[1] Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Shandong, Peoples R China

[2] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

[3] Curtin Univ Technol, Dept Math & Stat, Perth, WA 6845, Australia

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2015年 / 257卷

基金：

中国国家自然科学基金;

关键词：

Positive solution; First eigenvalue; Spectral analysis; Signed measure; Singularity; Fixed point index; MULTIPLE POSITIVE SOLUTIONS; BOUNDARY-VALUE-PROBLEMS; BLOW-UP; HEAT-EQUATIONS; SYSTEM; UNIQUENESS; EXISTENCE; EIGENVALUE;

D O I：

10.1016/j.amc.2014.12.068

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, by using the spectral analysis of the relevant linear operator and Gelfand's formula, we obtain some properties of the first eigenvalue of a fractional differential equation. Based on these properties, the fixed point index of the nonlinear operator is calculated explicitly and some sufficient conditions for the existence of positive solutions are established. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：252 / 263

页数：12

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