Abstract
In this work, we explore the boundedness and local and global asymptotic behavior of the solutions to a second-order difference formula of the exponential type zeta(n+1) = a + b zeta(n-1) + c zeta(n-1)e(-rho zeta n), where a, c, rho is an element of (0, infinity), b is an element of (0, 1) and the initials zeta(0), zeta(-1) are non-negative real numbers. Some other special cases are given. We provide two concrete numerical examples to confirm the theoretical results.