EXACT PERIODIC SOLUTIONS OF SECOND-ORDER DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENTS
2021 ◽
Vol 10
(9)
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pp. 3113-3128
Keyword(s):
In the paper is given a method of finding periodical solutions of the differential equation of the form $x''(t)+p(t)x''(t-1)=q(t)x([t])+f(t),$ where $[\cdot]$ denotes the greatest integer function, $p(t)$,$q(t)$ and $f(t)$ are continuous periodic functions of $t$. This reduces $n$-periodic soluble problem to a system of $n+1$ linear equations, where $n=2,3$. Furthermore, by using the well known properties of linear system in the algebra, all existence conditions for $2$ and $3$-periodical solutions are described, and the explicit formula for these solutions are obtained.
2007 ◽
Vol 326
(1)
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pp. 736-747
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Vol 146
(1)
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pp. 145-161
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1992 ◽
Vol 15
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pp. 339-346
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Vol 23
(4)
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pp. 763-778
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Vol 298
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pp. 298-307
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1993 ◽
Vol 24
(1)
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pp. 261-271
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