Multidimensional equation ∑lj=1(Djy)(Fjx) = γ(x) is considered. Here x ∈ ℝ1 and DJ : C∞(ℝ1, C m) → C∞(ℝ1, C n) are given differential linear operators. We build a theory of this equation via "common dynamics" of maps Fj. In particular, it is proved that the operator T0 : C∞(ℝ1, C m) → C∞(ℝ1, C n) with affine transformations Fjx = αjx + βj and differential linear operators Dj with constant coefficients is semi-Fredholm.
|Number of pages||9|
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|State||Published - 1 Jan 1997|
ASJC Scopus subject areas
- Applied Mathematics