Accession Number : AD0714148

Title :   Ordinary Differential Inequalities and Quasimonotonicity in Ordered Banach Spaces.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Walter,Wolfgang

Report Date : JAN 1970

Pagination or Media Count : 23

Abstract : A classical theorem on systems of ordinary differential inequalities states that (vector notation) v(0) = or < w(0), v' - f(t, v) = or < w' - f(t, w) in J = (0, T) implies v = or > w in J, if the function f(t, x) = (f sub 1, ..., f sub n) is quasimonotone increasing in x, i.e., if (f sub i)(t, x sub 1, ..., x sub n) is increasing in x sub j for i not equal to j. An appropriate concept of quasimonotonicity is formulated for arbitrary ordered Banach spaces, and the above theorem is generalized to the case of differential inequalities in ordered Banach spaces. (Author)

Descriptors :   (*DIFFERENTIAL EQUATIONS, INEQUALITIES), BANACH SPACE, BOUNDARY VALUE PROBLEMS, CAUCHY PROBLEM, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE