Abstract and Applied Analysis

Existence of Three Solutions for a Nonlinear Fractional Boundary Value Problem via a Critical Points Theorem

Chuanzhi Bai

Abstract

This paper is concerned with the existence of three solutions to a nonlinear fractional boundary value problem as follows: $(d/dt)((1/2){0}_{}{D}_{t}^{\alpha -1}{(}_{0}^{C}{D}_{t}^{\alpha }u(t))-(1/2){t}_{}{D}_{T}^{\alpha -1}{(}_{t}^{C}{D}_{T}^{\alpha }u(t)))+\lambda a(t)f(u(t))=0, \text{a}.\text{e}.\mathrm{ }t\in [0,T],$ $u(0)=u(T)=0,$ where $\alpha \in (1/2,1]$, and $\lambda$ is a positive real parameter. The approach is based on a critical-points theorem established by G. Bonanno.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 963105, 13 pages.

Dates
First available in Project Euclid: 5 April 2013

https://projecteuclid.org/euclid.aaa/1365168351

Digital Object Identifier
doi:10.1155/2012/963105

Mathematical Reviews number (MathSciNet)
MR2969986

Zentralblatt MATH identifier
1253.34008

Citation

Bai, Chuanzhi. Existence of Three Solutions for a Nonlinear Fractional Boundary Value Problem via a Critical Points Theorem. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 963105, 13 pages. doi:10.1155/2012/963105. https://projecteuclid.org/euclid.aaa/1365168351

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