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1
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On meromorphic functions for sharing two sets and three sets inm-punctured complex plane

100%
Xu H.-Y., Zheng X.-M., Wang H.
Open Mathematics
|
2016
|
tom 14
|
nr 1
913-924
EN
In this article, we study the uniqueness problem of meromorphic functions in m-punctured complex plane Ω and obtain that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 9, such that any two admissible meromorphic functions f and g in Ω must be identical if f, g share S1, S2 I M in Ω.
2
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Uniqueness of meromorphic functions sharing two finite sets

100%
Chen J.-F.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1244-1250
EN
We prove uniqueness theorems of meromorphic functions, which show how two meromorphic functions are uniquely determined by their two finite shared sets. This answers a question posed by Gross. Moreover, some examples are provided to demonstrate that all the conditions are necessary.
3
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Properties of the set of positive solutions to Dirichlet boundary value problems with time singularities

88%
Rachůnková I., Staněk S.
Open Mathematics
|
2013
|
tom 11
|
nr 1
112-132
EN
The paper investigates the structure and properties of the set S of all positive solutions to the singular Dirichlet boundary value problem u″(t) + au′(t)/t − au(t)/t 2 = f(t, u(t),u′(t)), u(0) = 0, u(T) = 0. Here a ∈ (−∞,−1) and f satisfies the local Carathéodory conditions on [0,T]×D, where D = [0,∞)×ℝ. It is shown that S c = {u ∈ S: u′(T) = −c} is nonempty and compact for each c ≥ 0 and S = ∪c≥0 S c. The uniqueness of the problem is discussed. Having a special case of the problem, we introduce an ordering in S showing that the difference of any two solutions in S c,c≥ 0, keeps its sign on [0,T]. An application to the equation v″(t) + kv′(t)/t = ψ(t)+g(t, v(t)), k ∈ (1,∞), is given.
4
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System of fractional differential equations with Erdélyi-Kober fractional integral conditions

75%
Thongsalee N., Laoprasittichok S., Ntouyas S. K., Tariboon J.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
In this paper we study existence and uniqueness of solutions for a system consisting from fractional differential equations of Riemann-Liouville type subject to nonlocal Erdélyi-Kober fractional integral conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. Examples illustrating our results are also presented.
5
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Two-point boundary value problems for the generalized Bagley-Torvik fractional differential equation

63%
Staněk S.
Open Mathematics
|
2013
|
tom 11
|
nr 3
574-593
EN
We investigate the fractional differential equation u″ + A c D α u = f(t, u, c D μ u, u′) subject to the boundary conditions u′(0) = 0, u(T)+au′(T) = 0. Here α ∈ (1, 2), µ ∈ (0, 1), f is a Carathéodory function and c D is the Caputo fractional derivative. Existence and uniqueness results for the problem are given. The existence results are proved by the nonlinear Leray-Schauder alternative. We discuss the existence of positive and negative solutions to the problem and properties of their derivatives.
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