Asymptotic behavior for non-oscillatory solutions of difference equations with several delays in the neutral term

摘要

In this paper, we first consider difference equations with several delays in the neutral term of the form * $$Deltaleft(y_{n}+sum_{i=1}^{L}p_{i}y_{n-{k_{i}}}-sum_{j=1}^{M}r_{j}y_{n-{rho_{j}}}right)+q_{n}y_{n-tau}=0quad mbox{for} ninmathbb{Z}^{+}(0),$$ study various cases of coefficients in the neutral term and obtain the asymptotic behavior for non-oscillatory solution of (*) under some hypotheses. Moreover, we consider reaction-diffusion difference equations with several delays in the neutral term of the form $$begin{array}{l}Delta_{1}left(u_{n,m}+displaystyle sum_{i=1}^{L}p_{i}u_{n-{k_{i}},m}-displaystyle sum_{j=1}^{M}r_{j}u_{n-{rho_{j}},m}right)+q_{n,m}u_{n-tau,m}[18pt]quad {}=a^{2}Delta_{2}^{2}u_{n+1,m-1}end{array}$$ for (n,m)∈?+(0)×Ω, study various cases of coefficients in the neutral term and obtain the asymptotic behavior for non-oscillatory solution under some hypotheses.