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Multiplicity of positive solutions of a class of nonlinear fractional differential equations

✍ Scribed by Jian-Ping Sun; Ya-Hong Zhao

Publisher: Elsevier Science
Year: 2005
Tongue: English
Weight: 337 KB
Volume: 49
Category: Article
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2005.01.006

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✦ Synopsis

This paper is concerned with the nonlinear fractional differential equation

where L(D) = D ~ -a~_lD s,~-1 ..... aiD ~1, 0 < sl < s2 < ... < s~ < 1, and aj > 0, j = 1,2,... ,n-1. Some results are obtained for the existence, nonexistence, and multiplicity of positive solutions of the above equation by using Krasnoselskii's fixed-point theorem in a cone. In particular, it is proved that the above equation has N positive solutions under suitable conditions, where N is an arbitrary positive integer. (~) 2005 Elsevier Ltd. All rights reserved.

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