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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/792689 |
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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |