Convergence of the solutions for the equation x(iv)+ax ⃛+bx¨+g(x˙)+h(x)=p(t,x,x˙,x¨,x ⃛)
This paper is concerned with differential equations of the formx(iv)+ax ⃛+bx¨+g(x˙)+h(x)=p(t,x,x˙,x¨,x ⃛)where a, b are positive constants and the functions g, h and p are continuous in their respective arguments, with the function h not necessarily differentiable. By introducing a Lyapunov function...
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| Format: | Article |
| Language: | English |
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Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171288000882 |
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| _version_ | 1832558475040784384 |
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| author | Anthony Uyi Afuwape |
| author_facet | Anthony Uyi Afuwape |
| author_sort | Anthony Uyi Afuwape |
| collection | DOAJ |
| description | This paper is concerned with differential equations of the formx(iv)+ax ⃛+bx¨+g(x˙)+h(x)=p(t,x,x˙,x¨,x ⃛)where a, b are positive constants and the functions g, h and p are continuous in their respective arguments, with the function h not necessarily differentiable. By introducing a Lyapunov function, as well as restricting the incrementary ratio η−1{h(ζ+η)−h(ζ)}, (η≠0), of h to a closed sub-interval of the Routh-Hurwitz interval, we prove the convergence of solutions for this equation. This generalizes earlier results. |
| format | Article |
| id | doaj-art-aff52ab215ad465ea4a0384aba23618e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1988-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-aff52ab215ad465ea4a0384aba23618e2025-02-03T01:32:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-0111472773310.1155/S0161171288000882Convergence of the solutions for the equation x(iv)+ax ⃛+bx¨+g(x˙)+h(x)=p(t,x,x˙,x¨,x ⃛)Anthony Uyi Afuwape0Department of Mathematics, University of Ife, Ile-lfe, NigeriaThis paper is concerned with differential equations of the formx(iv)+ax ⃛+bx¨+g(x˙)+h(x)=p(t,x,x˙,x¨,x ⃛)where a, b are positive constants and the functions g, h and p are continuous in their respective arguments, with the function h not necessarily differentiable. By introducing a Lyapunov function, as well as restricting the incrementary ratio η−1{h(ζ+η)−h(ζ)}, (η≠0), of h to a closed sub-interval of the Routh-Hurwitz interval, we prove the convergence of solutions for this equation. This generalizes earlier results.http://dx.doi.org/10.1155/S0161171288000882Routh-Hurwitz intervalLyapunov function. |
| spellingShingle | Anthony Uyi Afuwape Convergence of the solutions for the equation x(iv)+ax ⃛+bx¨+g(x˙)+h(x)=p(t,x,x˙,x¨,x ⃛) International Journal of Mathematics and Mathematical Sciences Routh-Hurwitz interval Lyapunov function. |
| title | Convergence of the solutions for the equation x(iv)+ax ⃛+bx¨+g(x˙)+h(x)=p(t,x,x˙,x¨,x ⃛) |
| title_full | Convergence of the solutions for the equation x(iv)+ax ⃛+bx¨+g(x˙)+h(x)=p(t,x,x˙,x¨,x ⃛) |
| title_fullStr | Convergence of the solutions for the equation x(iv)+ax ⃛+bx¨+g(x˙)+h(x)=p(t,x,x˙,x¨,x ⃛) |
| title_full_unstemmed | Convergence of the solutions for the equation x(iv)+ax ⃛+bx¨+g(x˙)+h(x)=p(t,x,x˙,x¨,x ⃛) |
| title_short | Convergence of the solutions for the equation x(iv)+ax ⃛+bx¨+g(x˙)+h(x)=p(t,x,x˙,x¨,x ⃛) |
| title_sort | convergence of the solutions for the equation x iv ax ⃛ bx¨ g x˙ h x p t x x˙ x¨ x ⃛ |
| topic | Routh-Hurwitz interval Lyapunov function. |
| url | http://dx.doi.org/10.1155/S0161171288000882 |
| work_keys_str_mv | AT anthonyuyiafuwape convergenceofthesolutionsfortheequationxivaxbxgxhxptxxxx |