Experimental validation is carried out using control-based continuation to obtain the experimental frequency response, including its unstable branch.
By application of the Manásevich-Mawhin continuation theorem, we obtain the existence of a positive periodic solution for this equation.
Finally, we make use of the Pontragin maximum principle and the unique continuation property to obtain the bang-bang property for optimal controls to this problem.
In Section 2, we first analyze qualitative properties of the generalized neutral operator A which will be helpful for further studies of differential equations with this neutral operator; in Section 3, by Mawhin's continuation theorem, we obtain the existence of periodic solutions for the generalized neutral Rayleigh equation with variable parameter.
The generalized differential quadrature (GDQ) method and pseudo-arc length continuation are employed to obtain the postbuckling load-deflection curves of nanoplates with various edge supports.
Upward continuation can be used to obtain the regional field either empirically or using some hypothesis about the geology.
In Sect. 2 we give a prior estimate and obtain the proof of Theorem 1.1 by applying the homotopy continuation method.
To obtain the existence of positive ω -periodic solutions of system (2), we will use the continuation theorem.
In [15], Lu, Li and Su applied the homotopy continuation method to give a constructive proof of Mawhin's continuation theorem in [20], which can be used to obtain the periodic solutions by track along a (C^{1}) trajectory.
Hence, in this paper, we will study system (1.1) and obtain the existence of periodic solutions by using the generalization of Mawhin's continuation theorem.
