对角化方法在向量非线性积分微分方程Robin边值问题中的应用  

Application of the Diagonalization Method in the Robin Boundary Value Problem for the Vector Nonlinear Integro-differential Equations

作　　者：林苏榕[1] 

机构地区：[1]福建广播电视大学计算机系,福州350003

出　　处：《数学物理学报（A辑）》2009年第2期406-415,共10页Acta Mathematica Scientia

摘　　要：纯量的积分微分方程奇摄动边值问题已被广泛地用微分不等式的方法研究过,然而,不可能推进这个方法到相应的非线性向量的积分微分方程上去,因此,对于n-维向量的积分微分方程来说,这个问题还没有完全解决.该文通过对角化方法研究这个非线性向量问题,在适当的条件下,证明解的存在性,同时也给出渐近的估计.The singularly perturbed boundary value problem of scalar integro-differential equations was studied extensively by the differential inequality method. However, it is impossible to carry this method over to a corresponding nonlinear vector integro-differential equation. Therefore, for n-dimensional vector integro-differential equations the problem has not be solved fully. Here, the author studys this nonlinear vector problem by diagonalization method. Under appropriate conditions the existence of solution is proved and the asymptotic estimate is given as well.

关 键 词：积分微分方程 奇异摄动 ROBIN边值问题 对角化方法. 

分 类 号：O175[理学—数学]