Average value problems in ordinary differential equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:249

Article

Chua, Seng-Kee

关键词: Initial value problems;    Existence and uniqueness;    Picard's iterations;    Caratheodory solution;    Signed measure;    Functional boundary value problems;   

DOI  :  10.1016/j.jde.2010.07.011

来源: Elsevier

【 摘 要 】

Using Schauder's fixed point theorem, with the help of an integral representation in 'Sharp conditions for weighted 1-dimensional Poincare inequalities', Indiana Univ. Math. J., 49 (2000) 143-175, by Chua and Wheeden, we obtain existence and uniqueness theorems and 'continuous dependence of average condition' for average value problem: y' = F(x, y), integral(b)(a) y(x) dv = y(0) where v is any probability measure on [a, b] under the usual conditions for initial value problem. We also extend our existence anti uniqueness theorems in the case where v is just a signed measure with v[a, b] not equal 0 and F : F subset of C[a, b] -> L(1) [a, b] is a continuous operator. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free