ASYMPTOTIC BEHAVIOR FOR NONOSCILLATORY SOLUTIONS OFREACTION-DIFFUSION DIFFERENTIAL EQUATIONS WITH SEVERAL DELAYS IN THE NEUTRAL TERM

• 作者: 徐美荣 时宝
• 来源期刊: 微分方程年刊：英文版
• 学科: 数学
• 关键词: 渐进线 微分方程 延迟 中性条件
• 年，卷（期）: 2004,（2）
• 页码范围: 180-193
• 页数: 14页
• 分类号: O175.12

摘要

In this paper, we first consider differential equations with several delays inthe neutral term of the form d/dt[y(t)+∑j=1^L piy(t-ki)-∑j=1^Mrjy(t-Pj)]+q(t)y(t-r)=0 for t∈R^+,(1^*) study various cases of coefficients in the neutral term and obtain the asymptotic behavior for nonoscillatory solution of (1") under some hypotheses. Moreover,we consider reaction-diffusion differential equations with several delays in the neutral term of the form α/αt[u(t,x)+∑i=1^L piu(t-ki,x)-∑j=1^M rju(t-Pj,x)]+q(t,x)u(t-r,x)=a^2△u(t,x)for (t,x)∈R^+ ×Ω. We also study various cases of coefficients in the neutral term and obtain the asymptotic behavior for nonoscillatory solutionun of (2^*)under some hypotheses.