摘要
本文研究时间变量是周期的反应扩散方程在非局部边值条件下周期解的存在性及其一般时变解的渐近性态；研究时间变量是周期的反应扩散方程组在非局部边值条件下周期解或周期拟解的存在性及其一般时变解的渐近性态．全文由三章组成。
在第一章，建立带非局部边值条件的单个反应扩散方程周期解的存在性及其局部渐近性态的上、下解方法。
在第二章，应用第一章的结果建立带非局部边值条件的反应扩散方程组周期解或周期拟解的存在性及其局部渐近性态的上、下解方法．分三种类型讨论：(1)拟单调不减系统；(2)混拟单调系统；(3)非拟单调2—系统．我们还将非局部边值条件中的核函数K_1(x，y)推广到不必定号的情况，对混拟单调反应扩散系统周期拟解的存在性及其局部渐近性态获得了类似的上、下解方法。
最后，在第三章应用本文的结果讨论了带非局部边值条件的Logistic方程正周期解的存在性及其渐近性态。
In this thesis we study the existence of periodic solutions and the asymptotic behavior of general time-dependent solutions for periodic reaction-diffusion equations with nonlocal boundary value conditions, the existence of periodic solutions or periodic quasisolutions and the asymptotic behavior of general time-dependent solutions for periodic reaction-diffusion systems with nonlocal boundary value conditions. The whole thesis is made up of three chapters.
In Chapter 1, we establish the upper and lower solutions method of the existence of periodic solutions and the local asymptotic behavior for scalar periodic reaction-diffusion equations with nonlocal boundary value conditions.
In Chapter 2, we apply the results of Chapter 1 to establish the upper and lower solutions method of the existence of periodic solutions or periodic quasisolutions and the local asymptotic behavior for periodic reaction-diffusion systems with nonlocal boundary value conditions. Three cases will be investigated: (1) Quasimonotone nondecreasing systems; (2) Mixed quasimonotone systems; (3) A nonquasimonotone 2-system. As an extension, we shall also consider similar problems for mixed quasimonotone reaction-diffusion systems with nonlocal boundary value conditions which kernel Ki(x,y) is alternating sign.
Finally, in Chapter 3, we use the above results to investigate the existence of positive periodic solutions and asymptotic behavior of solutions for the logistic equation with nonlocal boundary value conditions.
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