Necessary and sufficient conditions for eventually vanishing oscillatory solutions of functional equations with small delays
Necessary and sufficient conditions are found for all oscillatory solutions of the equation (rn−1(t)(rn−2(t)(−−−(r2(t)(r1(t)y′(t)))−−−)))+a(t)h(y(g(t)))=b(t) to approach zero. Sufficient conditions are also given to ensure that all solutions of this equation are unbounded.
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1978-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171278000307 |
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| _version_ | 1832564119912316928 |
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| author | Bhagat Singh |
| author_facet | Bhagat Singh |
| author_sort | Bhagat Singh |
| collection | DOAJ |
| description | Necessary and sufficient conditions are found for all oscillatory solutions of the equation (rn−1(t)(rn−2(t)(−−−(r2(t)(r1(t)y′(t)))−−−)))+a(t)h(y(g(t)))=b(t) to approach zero. Sufficient conditions are also given to ensure that all solutions of this equation are unbounded. |
| format | Article |
| id | doaj-art-456a673cd04d4fffbde59958ed5d3042 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1978-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-456a673cd04d4fffbde59958ed5d30422025-02-03T01:11:42ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251978-01-011326928310.1155/S0161171278000307Necessary and sufficient conditions for eventually vanishing oscillatory solutions of functional equations with small delaysBhagat Singh0Department of Mathematics, University of Wisconsin Center, 705 Viebahn Street, Manitowoc, Wisconsin 54220, USANecessary and sufficient conditions are found for all oscillatory solutions of the equation (rn−1(t)(rn−2(t)(−−−(r2(t)(r1(t)y′(t)))−−−)))+a(t)h(y(g(t)))=b(t) to approach zero. Sufficient conditions are also given to ensure that all solutions of this equation are unbounded.http://dx.doi.org/10.1155/S0161171278000307oscillatorynonoscillatorydelayfunctional. |
| spellingShingle | Bhagat Singh Necessary and sufficient conditions for eventually vanishing oscillatory solutions of functional equations with small delays International Journal of Mathematics and Mathematical Sciences oscillatory nonoscillatory delay functional. |
| title | Necessary and sufficient conditions for eventually vanishing
oscillatory solutions of functional equations with small delays |
| title_full | Necessary and sufficient conditions for eventually vanishing
oscillatory solutions of functional equations with small delays |
| title_fullStr | Necessary and sufficient conditions for eventually vanishing
oscillatory solutions of functional equations with small delays |
| title_full_unstemmed | Necessary and sufficient conditions for eventually vanishing
oscillatory solutions of functional equations with small delays |
| title_short | Necessary and sufficient conditions for eventually vanishing
oscillatory solutions of functional equations with small delays |
| title_sort | necessary and sufficient conditions for eventually vanishing oscillatory solutions of functional equations with small delays |
| topic | oscillatory nonoscillatory delay functional. |
| url | http://dx.doi.org/10.1155/S0161171278000307 |
| work_keys_str_mv | AT bhagatsingh necessaryandsufficientconditionsforeventuallyvanishingoscillatorysolutionsoffunctionalequationswithsmalldelays |