ANALYSIS OF SYSTEMS OF DIFFERENTIAL EQUATIONS HAVING SEVERAL NONLOCAL TERMS AND APPLICATIONS

首先，我们研究了人口规模结构模型，其中增长率、死亡率和生育率取决于人口规模和总人口权重。我们得到了解的存在、表示和唯一性。利用Schauder不动点定理，我们得到了一般模型解的存在性。为了独特性，我们对死亡率和生育率施加了一些更强的条件。不幸的是，目前还不知道是否可以消除更强的条件。这一结果发表在《J.Math.Anal.Appl.》杂志上。接下来，我们研究了一个一般的大小结构种群动力学的依赖于时间的模型，其中增长率取决于大小和时间。我们得到了解的存在性、正性和唯一性。时间依赖模型的研究是考虑非线性收获问题所必需的。事实上，我们将结果应用于一个大小结构种群模型的非线性收获问题。我们的模型具有只依赖于时间的收获率，但增长率依赖于大小和时间，生育率依赖于加权的总人口.我们在2004年在佛罗里达举行的国际会议上介绍了这一结果.进一步，我们发展了由多值函数描述的具有非局部项的非线性传输方程的理论，并将其应用于肌肉收缩的非线性四状态模型.在此，我们不仅得到了解的存在唯一性结果，而且得到了解的支撑性和有界性的结果.研究结果将发表在《高级数学科学分析》杂志上。

First, we have investigated size structured population models where the growth rate, the mortality rate and the fertility rate depend on size and total population weighted differently each other. We obtained the existence, the representation, and the uniqueness of solutions. By using Schauder's fixed point theorem, we obtained the existence of solutions in a general model. For the uniqueness, we imposed some stronger conditions on the mortality rate and the fertility rate. Unfortunately, it is not known whether the stronger conditions can be removed or not. The results are published in the journal, J.Math.Anal.Appl.Next, we have investigated a general time-dependent model of size structured population dynamics, where the growth rate depends on the size and time. We obtained the existence, positivity, and the uniqueness of solutions. The study of the time dependent model is needed to consider nonlinear harvesting problems.In fact, we applied the results to a nonlinear harvesting problem of size structured population models. Our model has the harvesting rate depending only on time, but the growth rate depends on the size and time and the fertility rate depends on the weighted total population.We gave a presentation about this result at the international conference held at Florida in 2004.Further, we have developed the theory of nonlinear transport equations with nonlocal terms prescribed by a multi-valued function and applied the results to nonlinear four state models of muscle contraction.Here, we obtained not only the existence and uniqueness results, but also the results of the support and the boundedness of the solution. The results will be published in the journal, Adv.Math.Sci.Anal.