Existence and Global Asymptotic Behavior of Positive Solutions for Nonlinear Fractional Dirichlet Problems on the Half-Line
We are interested in the following fractional boundary value problem: Dαu(t)+atuσ=0, t∈(0,∞), limt→0t2-αu(t)=0, limt→∞t1-αu(t)=0, where 1<α<2, σ∈(-1,1), Dα is the standard Riemann-Liouville fractional derivative, and a is a nonnegative continuous function on (0,∞) satisfying some appropriate...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/537971 |
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| Summary: | We are interested in the following fractional boundary value problem: Dαu(t)+atuσ=0, t∈(0,∞), limt→0t2-αu(t)=0, limt→∞t1-αu(t)=0, where 1<α<2, σ∈(-1,1), Dα is the standard Riemann-Liouville fractional derivative, and a is a nonnegative continuous function on (0,∞) satisfying some appropriate assumptions related to Karamata regular variation theory. Using the Schauder fixed point theorem, we prove the existence and the uniqueness of a positive solution. We also give a global behavior of such solution. |
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| ISSN: | 1085-3375 1687-0409 |