摘要：Firstly, sufficient conditions for nonexistence of an ω-periodic solution of the equation x ( n + 1 ) + a 0 ( n ) x ( n ) = b ( n ) are presented. Then, sufficient conditions under which every solution of the above equation is asymptotically ω-periodic are given. Next, the results obtained for the first-order difference equation are generalized for the higher-order nonhomogeneous linear difference equation ∑ i = 0 k a i ( n ) x ( n + i ) = b ( n ) . Finally, the periodic and asymptotically periodic solutions of this equation are investigated. Many examples illustrate the results given. MSC:39A11, 39A10.
关键词：nonhomogeneous linear difference equation ; asymptotically periodic solution
