文章基本信息

标题：Existence on positive solutions for boundary value problems of nonlinear fractional differential equations with p -Laplacian
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作者：Hongling Lu ; Zhenlai Han ; Shurong Sun 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2013
卷号：2013
期号：1
页码：30
DOI：10.1186/1687-1847-2013-30
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we study the existence of positive solutions for the nonlinear fractional boundary value problem with a p-Laplacian operator D 0 + β ( ϕ p ( D 0 + α u ( t ) ) ) = f ( t , u ( t ) ) , 0 1 , ϕ p − 1 = ϕ q , 1 / p + 1 / q = 1 , and f ( t , u ) ∈ C ( [ 0 , 1 ] × [ 0 , + ∞ ) , [ 0 , + ∞ ) ) . By the properties of Green’s function, the Guo-Krasnosel’skii fixed-point theorem, the Leggett-Williams fixed-point theorem, and the upper and lower solutions method, some new results on the existence of positive solutions are obtained. As applications, examples are presented to illustrate the main results. MSC:34A08, 34B18, 35J05.
关键词：fractional boundary value problem ; positive solution ; upper and lower solutions ; fixed-point theorems ; p -Laplacian operator