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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171288000882 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |