Displaying similar documents to “The Dirichlet problem for a parabolic semilinear differential equation in an unbounded domain.”

L 2 discrepancy of generalized Zaremba point sets

Henri Faure, Friedrich Pillichshammer (2011)

Journal de Théorie des Nombres de Bordeaux

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We give an exact formula for the L 2 discrepancy of a class of generalized two-dimensional Hammersley point sets in base b , namely generalized Zaremba point sets. These point sets are digitally shifted Hammersley point sets with an arbitrary number of different digital shifts in base b . The Zaremba point set introduced by White in 1975 is the special case where the b shifts are taken repeatedly in sequential order, hence needing at least b b points to obtain the optimal order of L 2 discrepancy....

Existence criteria for positive solutions of a nonlinear difference inequality

Sui Cheng, Guang Zhang (2000)

Annales Polonici Mathematici

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This paper is concerned with a class of nonlinear difference inequalities which include many different classes of difference inequalities and equations as special cases. By means of a Riccati type transformation, necessary and sufficient conditions for the existence of eventually positive solutions and positive nonincreasing solutions are obtained. Various type of comparison theorems are also derived as applications, which extends many theorems in the literature.