Existence of Periodic Solution for a Class of Linear Third Order ODE
In this paper, we will consider third order linear differential equation y 000 + αy00 + βy0 + γy + f(t, y) = e(t), where α, β, γ are constant coefficients, f(t, y) is continuous, e(t) is discontinuous, and f and e are periodic functions with respect to t of period w. We will introduce sufficie...
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| Format: | Article |
| Language: | English |
| Published: |
Islamic Azad University
2009-03-01
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| Series: | Journal of Mathematical Extension |
| Online Access: | http://ijmex.com/index.php/ijmex/article/view/59 |
| Summary: | In this paper, we will consider third order linear differential
equation
y
000 + αy00 + βy0 + γy + f(t, y) = e(t),
where α, β, γ are constant coefficients, f(t, y) is continuous, e(t)
is discontinuous, and f and e are periodic functions with respect
to t of period w. We will introduce sufficient conditions under
which the above equation have at least one non-trivial periodic
solution of period w. We will see that under the so called conditions,
all the solutions of the equation will be bounded. It must be
mentioned that e in this equation is called “controller” in the engineering
problems and it was always considered to be continuous
to ensure us that periodic solution exists. In this paper, we will
show the existence of periodic solution without supposing that e
to be continuous. |
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| ISSN: | 1735-8299 1735-8299 |