Strukturální vlastnosti jistých grup prostorů řešení lineárních homogenních diferenciálních rovnic třetího řádu
| Title in English | Structural properties of certain groups of solution spaces of the third order linear homogeneous different.equations |
|---|---|
| Authors | |
| Year of publication | 2012 |
| Type | Article in Proceedings |
| Conference | Acta mathematica 15, ed. PRÍRODOVEDEC, publ. č. 515 |
| MU Faculty or unit | |
| Citation | |
| Field | Pedagogy and education |
| Keywords | Differential equation; solution spaces of homogeneous differential equations; solvable group. |
| Attached files | |
| Description | The article was created on the basis of scientific research in the area of interdisciplinary relations between algebra and the theory of differential equations with the aim to find deeper connections between these two branches. In the theory of linear differential equations there is the useful method for the generalization of the results for the second-order equations to the case of the n-th order equations, which is based on the solution of the problem for the third-order equations. Using a one-to-one correspondence between homogeneous differential equations and their solution spaces there is obtained the information about the solution spaces groups, specifically there is answered the question of solvability of solution spaces group of linear homogeneous differential equations, and there are expounded some of their other properties. |