On the existence of a periodic solution of a nonlinear ordinary differential equation
Consider a planar forced system of the following form {dxdt=μ(x,y)+h(t)dydt=−ν(x,y)+g(t), where h(t) and g(t) are 2π-periodic continuous functions, t∈(−∞,∞) and μ(x,y) and ν(x,y) are continuous and satisfy local Lipschitz conditions. In this paper, by using the Poincáre's operator we show...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171298001070 |
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| Summary: | Consider a planar forced system of the following form
{dxdt=μ(x,y)+h(t)dydt=−ν(x,y)+g(t),
where
h(t) and g(t) are 2π-periodic continuous functions, t∈(−∞,∞) and
μ(x,y)
and ν(x,y)
are continuous and satisfy local Lipschitz conditions. In this
paper, by using the Poincáre's operator we show that if we assume the condltions,
(C1), (C2)
and (C3)
(see Section 2), then there is at least one 2π-periodic
solution. In conclusion, we provide an explicit example which is not in any class
of known results. |
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| ISSN: | 0161-1712 1687-0425 |