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2012 Existence of Three Solutions for a Nonlinear Fractional Boundary Value Problem via a Critical Points Theorem
Chuanzhi Bai
Abstr. Appl. Anal. 2012(SI01): 1-13 (2012). DOI: 10.1155/2012/963105

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.

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Chuanzhi Bai. "Existence of Three Solutions for a Nonlinear Fractional Boundary Value Problem via a Critical Points Theorem." Abstr. Appl. Anal. 2012 (SI01) 1 - 13, 2012. https://doi.org/10.1155/2012/963105

Information

Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1253.34008
MathSciNet: MR2969986
Digital Object Identifier: 10.1155/2012/963105

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI01 • 2012
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