An Explicit Criterion for the Existence of Positive Solutions of the Linear Delayed Equation x˙(t)=−c(t)x(t−τ(t))
The paper investigates an equation with single delay ẋ(t)=-c(t)x(t-τ(t)), where τ:[t0-r,∞)→(0,r], r>0, t0∈R, and c:[t0-r,∞)→(0,∞) are continuous functions, and the difference t-τ(t) is an increasing function. Its purpose is to derive a new explicit integral criterion for the existence of a posit...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/561902 |
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| author | J. Baštinec J. Diblík Z. Šmarda |
| author_facet | J. Baštinec J. Diblík Z. Šmarda |
| author_sort | J. Baštinec |
| collection | DOAJ |
| description | The paper investigates an equation with single delay ẋ(t)=-c(t)x(t-τ(t)), where τ:[t0-r,∞)→(0,r], r>0, t0∈R, and c:[t0-r,∞)→(0,∞) are continuous functions, and the difference t-τ(t) is an increasing function. Its purpose is to derive a new explicit integral criterion for the existence of a positive solution in terms of c and τ. An overview of known relevant criteria is provided, and relevant comparisons are also given. |
| format | Article |
| id | doaj-art-ebce9264dbad4497aad5be2c308cd50b |
| 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-ebce9264dbad4497aad5be2c308cd50b2025-02-03T06:01:10ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/561902561902An Explicit Criterion for the Existence of Positive Solutions of the Linear Delayed Equation x˙(t)=−c(t)x(t−τ(t))J. Baštinec0J. Diblík1Z. Šmarda2Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 616 00 Brno, Czech RepublicDepartment of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 616 00 Brno, Czech RepublicDepartment of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 616 00 Brno, Czech RepublicThe paper investigates an equation with single delay ẋ(t)=-c(t)x(t-τ(t)), where τ:[t0-r,∞)→(0,r], r>0, t0∈R, and c:[t0-r,∞)→(0,∞) are continuous functions, and the difference t-τ(t) is an increasing function. Its purpose is to derive a new explicit integral criterion for the existence of a positive solution in terms of c and τ. An overview of known relevant criteria is provided, and relevant comparisons are also given.http://dx.doi.org/10.1155/2011/561902 |
| spellingShingle | J. Baštinec J. Diblík Z. Šmarda An Explicit Criterion for the Existence of Positive Solutions of the Linear Delayed Equation x˙(t)=−c(t)x(t−τ(t)) Abstract and Applied Analysis |
| title | An Explicit Criterion for the Existence of Positive Solutions of the Linear Delayed Equation x˙(t)=−c(t)x(t−τ(t)) |
| title_full | An Explicit Criterion for the Existence of Positive Solutions of the Linear Delayed Equation x˙(t)=−c(t)x(t−τ(t)) |
| title_fullStr | An Explicit Criterion for the Existence of Positive Solutions of the Linear Delayed Equation x˙(t)=−c(t)x(t−τ(t)) |
| title_full_unstemmed | An Explicit Criterion for the Existence of Positive Solutions of the Linear Delayed Equation x˙(t)=−c(t)x(t−τ(t)) |
| title_short | An Explicit Criterion for the Existence of Positive Solutions of the Linear Delayed Equation x˙(t)=−c(t)x(t−τ(t)) |
| title_sort | explicit criterion for the existence of positive solutions of the linear delayed equation x˙ t c t x t τ t |
| url | http://dx.doi.org/10.1155/2011/561902 |
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