Abstract
We study the periodic solutions of the second-order differential equations of the form where the functions, , and are periodic of period in the variable t.
Highlights
Introduction and Statement of the MainResultsIn this paper we shall study the existence of periodic solutions of the second-order differential equation of the form ( ) x + 3xx + x3 + F (t ) x + x2 + G (t ) x + H (t ) = 0, (1)where the dot denotes derivative with respect to the time t, and the functions F (t ), G (t ) and H (t ) are periodic of period 2π in the variable t
We study the periodic solutions of the second-order differential equations of the form
3π2 8, we obtain using Theorem 1 the periodic solution given in the statement of the corollary
Summary
In this paper we shall study the existence of periodic solutions of the second-order differential equation of the form ( ) x + 3xx + x3 + F (t ) x + x2 + G (t ) x + H (t ) = 0,. For ε ≠ 0 sufficiently small, this differential ( ) equation has a 2π -periodic solution x (t,ε ) =ε (21cos t − 7 sin t ) 20 + O ε 2. For ε ≠ 0 sufficiently small, this differential equation has a 2π -periodic solution ( ) ( ) x (t,ε ) = ε (−2 cos t +15sin t ) 31+ 2 cos t (cos t −1) + O ε 2.
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