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Springer International Publishing AG 2012

Abstract

In this article, we consider the existence of positive solutions of the (n - 1, 1) conjugate-type nonlocal fractional differential equation

[Equation not available: see fulltext.]

where α â[per thousand]¥ 2, [InlineEquation not available: see fulltext.] is the standard Riemann-Liouville derivative, [InlineEquation not available: see fulltext.] is a linear functional given by the Stieltjes integral, A is a function of bounded variation, and dA may be a changing-sign measure, namely the value of the linear functional is not assumed to be positive for all positive x. By constructing upper and lower solutions, some sufficient conditions for the existence of positive solutions to the problem are established utilizing Schauder's fixed point theorem in the case in which the nonlinearities f(t, x) are allowed to have the singularities at t = 0 and (or) 1 and also at x = 0.

AMS (MOS) Subject Classification: 34B15; 34B25.[PUBLICATION ABSTRACT]

Details

Title
Positive solutions of higher-order nonlinear fractional differential equations with changing-sign measure
Author
Wu, Jianwu; Zhang, Xinguang; Liu, Lishan; Wu, Yonghong
Pages
1-14
Publication year
2012
Publication date
May 2012
Publisher
Springer Nature B.V.
ISSN
1687-1839
e-ISSN
1687-1847
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
1313750963
Copyright
Springer International Publishing AG 2012