Asymptotic behavior of impulsive neutral delay differential equations with positive and negative coefficients of Euler form

作者：Jiang, Fangfang^*; Shen, Jianhua; Ji, Zhicheng

来源：Advances in Difference Equations, 2018, 2018(1): 83.

DOI：10.1186/s13662-018-1503-4

• Impulse
• Neutral differential equation
• Unbounded delay
• Positive and negative coefficients of Euler form
• Constant jump

In this paper, we are concerned with asymptotic properties of solutions for a class of neutral delay differential equations with forced term, positive and negative coefficients of Euler form, and constant impulsive jumps of the form
{[x(t) - C(t)g(x(tau(t)))]' + p(t)/t f'(x)(alpha t)) - O(t)/t f(x(beta t)) = h(t), t >= t(0) > 0, t not equal t(k),
x(t(k)(+)) - x(t(k)) = alpha(k), k is an element of z(+).
By constructing auxiliary functions and applying the technique of considering asymptotic properties of nonoscillatory and oscillatory solutions we establish some sufficient conditions to guarantee that every solution of the system tends to zero as t -> +infinity.

• 出版日期2018-3-6
• 单位杭州师范大学; 江南大学