Existence of positive solutions to a higher order singular boundary value problem with fractional q-derivatives
2013 ◽
Vol 16
(3)
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Keyword(s):
AbstractThe authors study the singular boundary value problem with fractional q-derivatives $\begin{gathered} - (D_q^\nu u)(t) = f(t,u),t \in (0,1), \hfill \\ (D_q^i u)(0) = 0,i = 0,...,n - 2,(D_q u)(1) = \sum\limits_{j = 1}^m {a_j (D_q u)(t_j ) + \lambda ,} \hfill \\ \end{gathered} $, where q ∈ (0, 1), m ≥ 1 and n ≥ 2 are integers, n − 1 < ν ≤ n, λ ≥ 0 is a parameter, f: (0, 1] × (0,∞) → [0,∞) is continuous, a i ≥ 0 and t i ∈ (0, 1) for i = 1, …,m, and D qν is the q-derivative of Riemann-Liouville type of order ν. Sufficient conditions are obtained for the existence of positive solutions. Their analysis is mainly based on a nonlinear alternative of Leray-Schauder.
2005 ◽
Vol 29
(2)
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pp. 235-247
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2001 ◽
Vol 162
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pp. 127-148
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2004 ◽
Vol 47
(1)
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pp. 1-13
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2007 ◽
Vol 325
(1)
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pp. 517-528
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