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We are concerned with the uniqueness and existence of positive solutions for the following problem: ∆u+ λv1 = 0, x ∈ D, ∆v + λw2 = 0, x ∈ D, ∆w + λu3 = 0, x ∈ D, u = v = w = 0, x ∈ ∂D, where pi > 0(i = 1, 2, 3) and D is a smooth domain in R. If D is a ball in R, we prove the uniqueness of positive radially symmetric solution.
Article history: Received 11 March 2013 Received in revised form 14 August 2013 Available online 24 September 2013
Big Data is characterized by the five V's - of Volume, Velocity, Variety, Veracity and Value. Research on Big Data, that is, the practice of gaining insights from it, challenges the intellectual, process, and computational limits of an enterprise. Leveraging the correct and appropriate toolset requires careful consideration of a large software ecosystem.… (More)
We consider the stability of positive solutions to semilinear elliptic systems under a new general sublinear condition and its variants. Using the stability result and bifurcation theory, we prove the existence and uniqueness of positive solution and obtain the precise global bifurcation diagram of the system being a single monotone solution curve.
Twitter is widely used by businesses to communicate with and obtain feedback from their customers, almost in real time. Automated analysis is necessary to deal with the large volumes of tweets in a timely manner, and an insightful classification is a first step in this analysis. This paper presents an ensemble method that combines classifier outputs by… (More)