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Existence of periodic solutions
Mathematical Notes, 1997An apparatus for proving existence theorems for periodic solutions of equations with discontinuous right-hand side and differential inclusions is developed.
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Continuation of Periodic Solutions [PDF]
, 1992 In the last chapter, some local results about periodic solutions of Hamiltonian systems were presented. The systems contain a parameter, and the conditions under which a periodic solution can be continued in the parameter were discussed. Since Poincare used these ideas extensively, it has become known as Poincare’s continuation method.
Glen R. Hall, Kenneth R. Meyer
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Bifurcations of Periodic Solutions
2004In this chapter we will study bifurcations of periodic solutions in discontinuous systems of Filippov-type. The Poincare map, which is introduced in Section 9.1, converts the continuous-time system to a discrete map. Fixed points of piecewise linear maps, which represent periodic solutions of Filippov systems, are studied in Section 9.2.
Remco I. Leine, Henk Nijmeijer
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Stability of Periodic or Almost Periodic Solutions
2018In this chapter we study the asymptotic behavior of solutions as \({t } \rightarrow + \infty \), mainly in the case where \({h:}\ \mathbb {R} \rightarrow {H}\) is periodic or more generally almost periodic. As already mentioned in Remark 8.4.2, essentially nothing is known in this direction if f is non-linear.
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1989
INTRODUCTION Matsuoka studied in [7J, [8J, [9J the periodic solutions to a periodic system of differential equations en the plane. Based on the braiding information of known solutions, he obtained lower bounds for the number of extra periodic solutions, Some very interesting applications to subharmonic solutions of second order differential equations ...
Hai-Hua Huang +3 more
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INTRODUCTION Matsuoka studied in [7J, [8J, [9J the periodic solutions to a periodic system of differential equations en the plane. Based on the braiding information of known solutions, he obtained lower bounds for the number of extra periodic solutions, Some very interesting applications to subharmonic solutions of second order differential equations ...
Hai-Hua Huang +3 more
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A Myriad of Periodic Solutions
2016In this chapter we will consider two types of situations where the Poincare–Birkhoff Theorem can be successfully applied in order to prove the existence of several periodic solutions.
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2011
This chapter presents existence and stability of almost periodic solutions of the following system \( {\frac{dx(t)}{dt}} = A(t)x(t) + f(t,x(\theta_{\upsilon (t) - p1} ),x(\theta_{\upsilon (t) - p2} ), \ldots ,x(\theta_{\upsilon (t) - pm} )), \) (7.1) where \( x \in \mathbb{R}^{n} ,\;t \in \mathbb{R}, \) υ(t) = 1 if θ i ≤ t < θ i+1, i = …,-2,-1,0,1,2,…,
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This chapter presents existence and stability of almost periodic solutions of the following system \( {\frac{dx(t)}{dt}} = A(t)x(t) + f(t,x(\theta_{\upsilon (t) - p1} ),x(\theta_{\upsilon (t) - p2} ), \ldots ,x(\theta_{\upsilon (t) - pm} )), \) (7.1) where \( x \in \mathbb{R}^{n} ,\;t \in \mathbb{R}, \) υ(t) = 1 if θ i ≤ t < θ i+1, i = …,-2,-1,0,1,2,…,
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Existence of periodic solutions and almost periodic solutions
1991Yoshiyuki Hino +2 more
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2017
In the partial derivatives of X, the \( x_{i} \) are replaced by the periodic functions \( \varphi_{i} \). The \( \xi \) are thus determined by the linear equations with a right-hand side, whose coefficients are periodic functions.
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In the partial derivatives of X, the \( x_{i} \) are replaced by the periodic functions \( \varphi_{i} \). The \( \xi \) are thus determined by the linear equations with a right-hand side, whose coefficients are periodic functions.
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