非局部初值问题解的存在性定理  

Theorems about the Existence of Solutions to Problems with Nonlocal Initial Values

作　　者：王远弟[1] 

机构地区：[1]上海大学数学系,上海200436

出　　处：《数学学报（中文版）》2003年第3期513-522,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(19531060);上海市教委基金基金资助项目(02AK45)

摘　　要：近来非局部问题的研究日见增多,但涉及带非线性边界条件的初值问题文献 较少.本文目的在于证明一个半线性方程的齐次边值问题和一个非线性边界条件问题 解的存在性.主要使用半群,分数次幂函数空间,广义Poincare算子等工具.Recently, much work has been devoted to nonlocal problems. However, very little has been accomplished in the literature for nonlocal initial problems with nonlinear boundary conditions. It is the purpose of this paper to prove existence results for solutions to a semilinear second parabolic PDE with linear homogeneous boundary conditions and to another with nonlinear boundary conditions provided that the ordered upper and lower solutions are given. Semigroup, fractional order function spaces, and generalized Poincare operators play an important role in proving the existence of solutions.

关 键 词：非局部问题 非线性边界条件 抛物型方程 解 存在性 广义Poincaré算子 

分 类 号：O175.26[理学—数学]