Existence of subharmonic periodic solutions to a class of second-order non-autonomous neutral functional differential equations. (English) Zbl 1244.34091

Shu, Xiao-Bao; Lai, Yongzeng; Xu, Fei

Abstr. Appl. Anal. 2012, Article ID 404928, 26 p. (2012).

Summary: By introducing subdifferentiability of the lower semicontinuous convex function \(\varphi(x(t), x(t - \tau))\) and its conjugate function, as well as critical point theory and operator equation theory, we obtain the existence of multiple subharmonic periodic solutions to the following second-order nonlinear nonautonomous neutral nonlinear functional differential equation \[ x''(t) + x'' (t - 2\tau) + f(t, x(t), x(t - \tau), x(t - 2\tau)) = 0, ~x(0) = 0. \]

MSC:

34K13	Periodic solutions to functional-differential equations
58E05	Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
47N20	Applications of operator theory to differential and integral equations

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