Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 150, pp. 1-21.

Title: Existence of infinitely many periodic subharmonic solutions for
       nonlinear non-autonomous neutral differential equations
        
Authors: Xiao-Bao Shu (Hunan Univ., Changsha, China)
         Yongzeng Lai (Wilfrid Laurier Univ., Waterloo, Ontario, Canada)
         Fei Xu       (Wilfrid Laurier Univ., Waterloo, Ontario, Canada)

Abstract:
 In this article, we study the existence of an infinite number of
 subharmonic periodic solutions to a class of second-order neutral
 nonlinear functional differential equations. Subdifferentiability
 of lower semicontinuous convex functions $\varphi(x(t),x(t-\tau))$
 and the corresponding conjugate functions are constructed.
 By combining the critical point theory, Z2-group index theory
 and operator equation theory, we obtain the infinite number of
 subharmonic periodic solutions to such system.

Submitted  November 13, 2012. Published June 28, 2013.
Math Subject Classifications: 34K13, 34K40, 65K10.
Key Words: Subharmonic periodic solution; variational structure;
           operator equation;  critical point;  subdifferential;  
           neutral functional differential equation;  Z2-group; index theory.