Positive solutions for superlinear fractional boundary value problems

被引：0
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作者：
Imed Bachar
Habib Mâagli
机构：
[1] King Saud University,Mathematics Department, College of Science
[2] King Abdulaziz University,Department of Mathematics, College of Sciences and Arts
来源：
Advances in Difference Equations | / 2014卷
关键词：
fractional differential equations; boundary value problem; positive solutions; Green’s function; perturbation arguments;
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摘要：
We establish the existence, uniqueness, and global behavior of a positive solution for the following superlinear fractional boundary value problem: Dαu(x)=u(x)φ(x,u(x)), x∈(0,1), limx→0+Dα−1u(x)=−a, u(1)=b, where 1<α≤2, Dα is the standard Riemann-Liouville fractional derivative, a, b are nonnegative constants such that a+b>0 and φ(x,t) is a nonnegative continuous function in (0,1)×[0,∞) that is required to satisfy some appropriate conditions related to a certain class of functions Kα. Our approach is based on estimates of the Green’s function and on perturbation arguments.
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