Stability in mixed linear delay Levin-Nohel integro-dynamic equations on time scales
In this paper we use the contraction mapping theorem to obtain asymptotic stability results about the zero solution for the following mixed linear delay Levin-Nohel integro-dynamic equation x^{Δ}(t)+∫_{t-r(t)}^{t}a(t,s)x(s)Δs+b(t)x(t-h(t))=0, t∈[t₀,∞)∩T, where f^{△} is the △-derivative on T. A...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática
2019-03-01
|
| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/37758 |
| Summary: | In this paper we use the contraction mapping theorem to obtain asymptotic stability results about the zero solution for the following mixed linear delay Levin-Nohel integro-dynamic equation
x^{Δ}(t)+∫_{t-r(t)}^{t}a(t,s)x(s)Δs+b(t)x(t-h(t))=0, t∈[t₀,∞)∩T,
where f^{△} is the △-derivative on T. An asymptotic stability theorem with a necessary and sufficient condition is proved. The results obtained here extend the work of Dung <cite>d</cite>. In addition, the case of the equation with several delays is studied. |
|---|---|
| ISSN: | 0037-8712 2175-1188 |