Asymptotic behavior of solutions of mixed type impulsive neutral differential equations

作者：Tariboon Jessada^*; Ntouyas Sotiris K; Thaiprayoon Chatthai

来源：Advances in Difference Equations, 2014, 2014(1): 327.

DOI：10.1186/1687-1847-2014-327

• asymptotic behavior
• nonlinear neutral delay differential equation
• impulse
• Lyapunov functional

This paper investigates the asymptotic behavior of solutions of the mixed type neutral differential equation with impulsive perturbations %26lt;br%26gt;[x(t) + C(t - tau) - D(t)x(alpha t)]%26apos; + rho(t)f(x(t - delta)) + Q(t)/tx(beta t) = Q,0%26lt;t(0) %26lt;= t,t not equal t(k), %26lt;br%26gt;x(t(k)) = b(k)x(t(k)(-))+(1-b(k))(integral t(k-delta)(tk)P(s+delta)f(x(s))ds+integral(tk)(beta tk) Q((s/beta))/s x(s) ds) , k = 1,2,3, ... Sufficient conditions are obtained to guarantee that every solution tends to a constant as t -%26gt; infinity Examples illustrating the abstract results are also presented.

• 出版日期2014-12-22