一类非线性方程的Dirich Iet边值问题

研究具有非线性扰动的Dirichlet边值问题u"(t)=λu(t)+f(u)+g(t),u(0)=u(π)=0的经典解存在性问题.借助于求泛函临界点的方法来讨论经典解的存在性.不少作者用不动点定理来研究Dirichlet问题的弱解和经典解的存在性.这里的结果去掉了文献[4]～[6]中对f(x)作的有界性、非减性与limf(x)存在性假设.     

具正负系数的非齐次NDDE解的渐近性质

考虑具正负系数的非齐次NDDE其中解的渐近性质。在适当条件下,证明了上述方程所有解都趋向于一个常数。     

α-times Integrated Regularized Cosine Functions and Second Order Abstract Cauchy Problems

In this paper, a -times integrated C-regularized cosine functions and mild a -times integrated C-existence families of second order are introduced. Equivalences are proved among a -times integrated C-regularized cosine function for a linear operator A, C-wellposed of (a + l)-times abstract Cauchy problem and mild a -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C~1AC, they are also equivalent to A generating the a -times integrated C-regularized cosine function. The characterization of an exponentially bounded mild a -times integrated C-existence family of second order is given out in terms of a Laplace transform.     

一个具Logistic-型源和非线性信号产出的趋化系统解的渐近行为

考虑一个带增长源和非线性信号产出的趋化系统,在适当的参数假设之下,利用Lp先验估计方法和Moser迭代技巧等证明了该系统整体古典解的存在性和有界性。进一步,通过构造合适的Lyapunov泛函研究了有界解的渐近性质。     

α-times Integrated Regularized Cosine Functions and Second Order Abstract Cauchy Problens

In this paper, α -times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α -times integrated C-regularized cosine function for a linear operator A, C-wellposed of (α + 1)-times abstract Cauchy problem and mild α -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C-1AC, they are also equivalent to A generating the α -times integrated C-regularized cosine finction.The characterization of an exponentially botnded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.     

某一类一阶中立型线性非齐次方程的振动性

研究非齐次中立型线性微分差分方程的振动问题。借助于非齐次中立型微分方差分不等式的最终正解和最终负解的性质,来讨论方程(＊)的振动性。     

Asymptotic Behavior and Oscillation for Forced Odd Order Neutral Differential Equations

Consider the forced odd order neutral differential equations of the form     

一个肿瘤化疗数学模型的分析

这里考虑一个刻画血管化肿瘤的化学治疗的数学模型.该模型是一个偏微分方程系统的自由边界问题.系统的未知变量有：肿瘤细胞内部的药物浓度;对药物敏感的和具有耐药性的肿瘤细胞密度;肿瘤细胞运动的速度场;自由边界（即肿瘤边界）.本文对该模型进行严格的数学分析,从理论上探索对肿瘤成功治疗时药物浓度所满足的条件.     

Inverse Problem of a Tumor Model

This paper considers a model for the growth of a solid tumor with a single anticancer agent application.The model is a free boundary problem of a nonlinear reactiondiffusion-advection equation,where the free boundary is the surface of the tumor.Since multicellular spheroids are routinely used as in vitro( i.e.,outside live organisms)models of cancer growth and they can be observed and controlled in the laboratory,the following inverse problem is studied:given observed dynamics of tumor growth,a certain parameter is determined.The Lipschitz stability of solutions to the above-mentioned inverse problem is established,and this inverse problem is solved by control theory.Numerical methods for solving the inverse problem are also given.