Growth and oscillation properties of solutions of a fourth order linear difference equation

Abstract

Abstract For the fourth-order linear difference equation Δ 4 u n −2 = b n u n , with b n > 0 for all n , generalized zeros are defined, following Hartman [5], and two theorems are proved concerning separation of zeros of linearly independent solutions. Some preliminary results deal with non-oscillation and asymptotic behavior of solutions of this equation for various types of initial conditions. Finally, recessive solutions are defined, and results are obtained analogous to known results for recessive solutions of second-order difference equations.