Zhenlai Han, Hongling Lu, Shurong Sun, Dianwu Yang
Abstract:
In this article, we consider the following boundary-value problem
of nonlinear fractional differential equation with
-Laplacian operator
where
,
are real numbers,
are the standard Caputo fractional derivatives,
,
,
,
,
,
,
is a parameter,
and
are continuous.
By the properties of Green function and Schauder fixed point theorem,
several existence and nonexistence results for positive solutions,
in terms of the parameter
are obtained.
The uniqueness of positive solution on the parameter
is also studied.
Some examples are presented to illustrate the main results.
Submitted September 5, 2012. Published November 27, 2012.
Math Subject Classifications: 34A08, 34B18, 35J05.
Key Words: Fractional boundary-value problem; positive solution; cone;
Schauder fixed point theorem; uniqueness; p-Laplacian operator.
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Zhenlai Han School of Mathematical Sciences University of Jinan Jinan, Shandong 250022, China email: hanzhenlai@163.com | |
Hongling Lu School of Mathematical Sciences University of Jinan Jinan, Shandong 250022, China email: lhl4578@126.com | |
Shurong Sun School of Mathematical Sciences University of Jinan Jinan, Shandong 250022, China email: sshrong@163.com | |
Dianwu Yang School of Mathematical Sciences University of Jinan Jinan, Shandong 250022, China email: ss_yangdw@ujn.edu.cn |
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