Ordinary Differential Inequalities and Quasimonotonicity in Ordered Banach Spaces.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1970
- Accession Number
- AD0714148
Entities
People
- Wolfgang Walter
Organizations
- University of Wisconsin–Madison