Existence of periodic solutions for a type of linear difference equations with distributed delay

摘要

By employing primary algebraic techniques, we establish a necessary and sufficient condition for the existence of periodic solutions for a type of linear difference equations with distributed delay of the form Δ x ( n ) = ∑ k = - d 0 Δ k ζ ( n + 1 , k - 1 ) x ( n + k - 1 ) , n ≥ 1 . (*) Our approach is based on constructing an adjoint equation for (*) and proving that (*) and its adjoint equation have the same number of linearly independent periodic solutions. AMS Subject Classification: 39A11.