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.