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Displaying similar documents to “Oscillation of a nonlinear difference equation with several delays”

Global behavior of a third order rational difference equation

Raafat Abo-Zeid (2014)

Mathematica Bohemica

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In this paper, we determine the forbidden set and give an explicit formula for the solutions of the difference equation x n + 1 = a x n x n - 1 - b x n + c x n - 2 , n 0 where a , b , c are positive real numbers and the initial conditions x - 2 , x - 1 , x 0 are real numbers. We show that every admissible solution of that equation converges to zero if either a < c or a > c with ( a - c ) / b < 1 . When a > c with ( a - c ) / b > 1 , we prove that every admissible solution is unbounded. Finally, when a = c , we prove that every admissible solution converges to zero.

On a set of asymptotic densities

Pavel Jahoda, Monika Jahodová (2008)

Acta Mathematica Universitatis Ostraviensis

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Let = { p 1 , p 2 , , p i , } be the set of prime numbers (or more generally a set of pairwise co-prime elements). Let us denote A p a , b = { p a n + b m n { 0 } ; m , p does not divide m } , where a , b { 0 } . Then for arbitrary finite set B , B holds d p i B A p i a i , b i = p i B d A p i a i , b i , and d A p i a i , b i = 1 p i b i 1 - 1 p i 1 - 1 p i a i . If we denote A = 1 p b 1 - 1 p 1 - 1 p a p , a , b { 0 } , where is the set of all prime numbers, then for closure of set A holds cl A = A B { 0 , 1 } , where B = 1 p b 1 - 1 p p , b { 0 } .