# Describe the behavior after finding the gerneral solution

• Mar 7th 2010, 07:17 PM
onemore
Describe the behavior after finding the gerneral solution
Consider the difference equation $U_{n+4} - A^{4} U_n = 0 where A>0.$ Find the gerneral solution of this equation. Describe the behavior of solution with respect to oscillation, boundedness, periodicity, and asymptotics where (1) A<1 (2) A=1 (3)A>1.

$u_{i,n+1} = - \alpha\cdot u_{i,n} , \alpha = a^{4} , i=0,1,2,3$ (1)
$u_{i,n}= u_{i,0}\cdot (-\alpha)^{n}$ (2)
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