Annals of Functional Analysis

Eigenvalue problem for a class of nonlinear fractional differential equations

‎Zhenla Han‎, Jian Liu‎, Shurong Sun, and ‎Yige Zhao‎

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Abstract

‎In this paper, we study eigenvalue problem for a class of nonlinear fractional differential equations $$D^\alpha_{0^+}u(t)=\lambda f(u(t)),\quad 0 \lt t \lt 1,$$ $$u(0)=u(1)=u'(0)=u'(1)=0,$$ where $3 \lt \alpha\leq4$ is a real number, $D^\alpha_{0^+}$ is the Riemann-Liouville fractional derivative, $\lambda$ is a positive parameter and $f:(0,+\infty)\to(0,+\infty)$ is continuous. By the properties of the Green function and Guo-Krasnosel'skii fixed point theorem on cones, the eigenvalue intervals of the nonlinear fractional differential equation boundary value problem are considered, some sufficient conditions for the nonexistence and existence of at least one or two positive solutions for the boundary value problem are established. As an application, some examples are presented to illustrate the main results.

Article information

Source
Ann. Funct. Anal., Volume 4, Number 1 (2013), 25-39.

Dates
First available in Project Euclid: 12 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1399899834

Digital Object Identifier
doi:10.15352/afa/1399899834

Mathematical Reviews number (MathSciNet)
MR3004208

Subjects
Primary: 47A75
Secondary: 34A08: Fractional differential equations

Keywords
Fractional differential equation boundary value problem ‎positive solution fractional Green's function fixed point theorem eigenvalue problem

Citation

Sun, Shurong; Zhao‎, ‎Yige; Han‎, ‎Zhenla; Liu‎, Jian. Eigenvalue problem for a class of nonlinear fractional differential equations. Ann. Funct. Anal. 4 (2013), no. 1, 25--39. doi:10.15352/afa/1399899834. https://projecteuclid.org/euclid.afa/1399899834


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