【摘要】 利用上、下解方法及相应的单调迭代方法研究了一类反应项非单调的时滞反应扩散方程,构造了非单调反应项的上、下控制函数,并证明了所构造的函数满足L ipsch itz条件及单调性,克服了反应项非单调无法利用单调迭代方法的局限性。为讨论反应项非单调的微分方程提供了一种有效方法,并获得了此方程解的有界性及周期解存在唯一性的充分条件,推广了已有的一些结果。更多还原

【Abstract】 In this paper,bounded solution and periodic solution of reaction-diffusion equation with time delay are investigated.By constructing the upper and lower control function of the reaction function with non-monotone and using the method of upper and lower solutions,the authors demonstrate that the constructed function satisfy the Lipschits condition and monotont,and that it covercome the shortness of the reaction function with non-monotone.It is shown that if the reaction function in the system is non-monotone and the boundary value,then the system has a pair of coupled-upper and lower solutions,and the equation has a unique periodic solution.And some known results are widely used.更多还原