Asymptotic properties of Kneser type solutions for third order half-linear neutral difference equations

Abstract

The authors examine properties of positive solutions of the third order half-linear neutral difference equation ∆(a n ∆(b n (∆z n ) α )) + q n y α n+1 = 0, where z n = y n + p n y σ(n) . They show that the positive solutions are in fact Kneser type solutions and they provide upper and lower bounds that yield the rate of convergence to zero for such solutions. Examples are provided to illustrate the main results.