Existence Conditions for Bounded Solutions of Weakly Perturbed Linear Impulsive Systems
The weakly perturbed linear nonhomogeneous impulsive systems in the form ẋ=A(t)x + εA1(t)x + f(t), t∈R, t∉T:={τi}Z, Δx|t=τi=γi+εA1ix(τi-), τi∈T⊂R, γi∈Rn, and i∈Z are considered. Under the assumption that the generating system (for ε=0) does not have solutions bounded on the entire real axis...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/792689 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832562479111077888 |
|---|---|
| author | Alexander Boichuk Martina Langerová Jaroslava Škoríková |
| author_facet | Alexander Boichuk Martina Langerová Jaroslava Škoríková |
| author_sort | Alexander Boichuk |
| collection | DOAJ |
| description | The weakly perturbed linear nonhomogeneous impulsive systems in the form ẋ=A(t)x + εA1(t)x + f(t), t∈R, t∉T:={τi}Z, Δx|t=τi=γi+εA1ix(τi-), τi∈T⊂R, γi∈Rn, and i∈Z are considered. Under the assumption that the generating system (for ε=0) does not have solutions bounded on the entire real axis for some nonhomogeneities and using the Vishik-Lyusternik method, we establish conditions for the existence of solutions of these systems bounded on the entire real axis in the form of a Laurent series in powers of small parameter ε with finitely many terms with negative powers of ε, and we suggest an algorithm of construction of these solutions. |
| format | Article |
| id | doaj-art-87f091f4ff244530b3ed4b7753559269 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-87f091f4ff244530b3ed4b77535592692025-02-03T01:22:31ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/792689792689Existence Conditions for Bounded Solutions of Weakly Perturbed Linear Impulsive SystemsAlexander Boichuk0Martina Langerová1Jaroslava Škoríková2Institute of Mathematics, National Academy of Science of Ukraine, 01601 Kyiv, UkraineDepartment of Mathematics, University of Žilina, 01026 Žilina, SlovakiaDepartment of Mathematics, University of Žilina, 01026 Žilina, SlovakiaThe weakly perturbed linear nonhomogeneous impulsive systems in the form ẋ=A(t)x + εA1(t)x + f(t), t∈R, t∉T:={τi}Z, Δx|t=τi=γi+εA1ix(τi-), τi∈T⊂R, γi∈Rn, and i∈Z are considered. Under the assumption that the generating system (for ε=0) does not have solutions bounded on the entire real axis for some nonhomogeneities and using the Vishik-Lyusternik method, we establish conditions for the existence of solutions of these systems bounded on the entire real axis in the form of a Laurent series in powers of small parameter ε with finitely many terms with negative powers of ε, and we suggest an algorithm of construction of these solutions.http://dx.doi.org/10.1155/2011/792689 |
| spellingShingle | Alexander Boichuk Martina Langerová Jaroslava Škoríková Existence Conditions for Bounded Solutions of Weakly Perturbed Linear Impulsive Systems Abstract and Applied Analysis |
| title | Existence Conditions for Bounded Solutions of Weakly Perturbed Linear Impulsive Systems |
| title_full | Existence Conditions for Bounded Solutions of Weakly Perturbed Linear Impulsive Systems |
| title_fullStr | Existence Conditions for Bounded Solutions of Weakly Perturbed Linear Impulsive Systems |
| title_full_unstemmed | Existence Conditions for Bounded Solutions of Weakly Perturbed Linear Impulsive Systems |
| title_short | Existence Conditions for Bounded Solutions of Weakly Perturbed Linear Impulsive Systems |
| title_sort | existence conditions for bounded solutions of weakly perturbed linear impulsive systems |
| url | http://dx.doi.org/10.1155/2011/792689 |
| work_keys_str_mv | AT alexanderboichuk existenceconditionsforboundedsolutionsofweaklyperturbedlinearimpulsivesystems AT martinalangerova existenceconditionsforboundedsolutionsofweaklyperturbedlinearimpulsivesystems AT jaroslavaskorikova existenceconditionsforboundedsolutionsofweaklyperturbedlinearimpulsivesystems |