Systems of advance-delay differential-difference equations and transformation groups
A linear system of mixed-type differential difference equations is studied. A step derivation method and some conditions on an initial function are used to guarantee existence, uniqueness and smoothness of the solution. Further, a transformation group is defined on a complete countably normed s...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2016-12-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/311/abstr.html |
| _version_ | 1818519424742719488 |
|---|---|
| author | Serguei I. Iakovlev Valentina Iakovleva |
| author_facet | Serguei I. Iakovlev Valentina Iakovleva |
| author_sort | Serguei I. Iakovlev |
| collection | DOAJ |
| description | A linear system of mixed-type differential difference equations is studied.
A step derivation method and some conditions on an initial function are
used to guarantee existence, uniqueness and smoothness of the solution.
Further, a transformation group is defined on a complete countably normed
space of initial functions and the spectrum of the infinitesimal generator
of this group is studied.
The same technique applies to a linear system of retarded differential
difference equations. A problem to extend solutions of such a system to
the left on the real line is solved. |
| first_indexed | 2024-12-11T01:24:03Z |
| format | Article |
| id | doaj.art-c7cf7b99536c4410a1cfd28bb0211ac0 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-11T01:24:03Z |
| publishDate | 2016-12-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-c7cf7b99536c4410a1cfd28bb0211ac02022-12-22T01:25:37ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912016-12-012016311,116Systems of advance-delay differential-difference equations and transformation groupsSerguei I. Iakovlev0Valentina Iakovleva1 Univ. Simon Bolivar, Caracas, Venezuela Univ. Simon Bolivar, Caracas, Venezuela A linear system of mixed-type differential difference equations is studied. A step derivation method and some conditions on an initial function are used to guarantee existence, uniqueness and smoothness of the solution. Further, a transformation group is defined on a complete countably normed space of initial functions and the spectrum of the infinitesimal generator of this group is studied. The same technique applies to a linear system of retarded differential difference equations. A problem to extend solutions of such a system to the left on the real line is solved.http://ejde.math.txstate.edu/Volumes/2016/311/abstr.htmlAdvance-delay differential-difference equationsstep derivation methoduniquenesstransformation groupinfinitesimal generatorpoint spectrum |
| spellingShingle | Serguei I. Iakovlev Valentina Iakovleva Systems of advance-delay differential-difference equations and transformation groups Electronic Journal of Differential Equations Advance-delay differential-difference equations step derivation method uniqueness transformation group infinitesimal generator point spectrum |
| title | Systems of advance-delay differential-difference equations and transformation groups |
| title_full | Systems of advance-delay differential-difference equations and transformation groups |
| title_fullStr | Systems of advance-delay differential-difference equations and transformation groups |
| title_full_unstemmed | Systems of advance-delay differential-difference equations and transformation groups |
| title_short | Systems of advance-delay differential-difference equations and transformation groups |
| title_sort | systems of advance delay differential difference equations and transformation groups |
| topic | Advance-delay differential-difference equations step derivation method uniqueness transformation group infinitesimal generator point spectrum |
| url | http://ejde.math.txstate.edu/Volumes/2016/311/abstr.html |
| work_keys_str_mv | AT sergueiiiakovlev systemsofadvancedelaydifferentialdifferenceequationsandtransformationgroups AT valentinaiakovleva systemsofadvancedelaydifferentialdifferenceequationsandtransformationgroups |