Periodic solutions of asymptotically linear autonomous Newtonian systems with resonance

2012 ◽  
Vol 75 (10) ◽  
pp. 4033-4050 ◽  
Author(s):  
Justyna Fura
Keyword(s):  
Periodic Solutions ◽  
Asymptotically Linear ◽  
Newtonian Systems

scholarly journals Periodic solutions for a class of second-order differential delay equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xuan Wu ◽  
Huafeng Xiao
Keyword(s):  
Periodic Solutions ◽  
Index Theory ◽  
Second Order ◽  
Delay Equations ◽  
Asymptotically Linear ◽  
Differential Delay ◽  
Differential Delay Equations ◽  
Existence Of Periodic Solutions ◽  
The Difference

<p style='text-indent:20px;'>In this paper, we study the existence of periodic solutions of the following differential delay equations</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation} z^{\prime\prime}(t) = \sum\limits_{k = 1}^{M-1}(-1)^kf(z(t-k)), \notag \end{equation} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ f\in C(\mathbf{R}^N, \mathbf{R}^N) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ M,N\in \mathbf{N} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ M $\end{document}</tex-math></inline-formula> is odd. By making use of <inline-formula><tex-math id="M4">\begin{document}$ S^1 $\end{document}</tex-math></inline-formula>-geometrical index theory, we obtain an estimation about the number of periodic solutions in term of the difference between eigenvalues of asymptotically linear matrices at the origin and at infinity.</p>

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