الفهرس يوجد فقط 14 صفحة متاحة للعرض العام
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المستخلص
In this thesis we focus our work on the global asymptotic behavior of difference equations of the form:
x n + 1 = F(x n ,x n-1 ,...,x n-l ) G(x n ,x n-1 ,...,x n-k ) , n = 0, 1
where F, G are polynomials such that either F(x n ,x n - 1 ,...,x n-l ) contains terms of the form prod i = 1 to m x n-r 4 where 0 <= r_{i} <= l, 1 <= i <= m or G(x n ,x n - 1 ,...,x n-k ) contains terms of the form prod i = 1 to m x n-r i where 0 <= r_{i} <= k, 1 <= i <= m
We investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equations:
x n + 1 = Ax n-1 B+Cx n-2l x n-2k , n = 0, 1
x n + 1 = Ax n-1 B+C prod i=l ^ k x n-2i , n = 0, 1
where A, B, C are nonnegative real numbers and I, k are nonnegative integers, l <= k Finally, we investigate the global attractivity, periodic nature, oscillation and the boundedness of the positive solutions of the difference equation
x n + 1 = A prod i=1 ^ k x n-2i-1 B+C prod i=1 ^ k-1 x n-2i , n = 0, 1
where A, B, C are nonnegative real numbers and l, k are nonnegative integers, l < k
Keywords: Difference equation, periodic solution, globally asymptotically stable.