Existence of infinitely many periodic subharmonic solutions for nonlinear non-autonomous neutral differential equations

• Main Authors: Xiao-Bao Shu, Yongzeng Lai, Fei Xu
• Format: Article
• Language: English
• Published: Texas State University 2013-06-01
• Series: Electronic Journal of Differential Equations
• Subjects: Subharmonic periodic solution; variational structure; operator equation; critical point; subdifferential; neutral functional differential equation; Z2-group; index theory
• Online Access: http://ejde.math.txstate.edu/Volumes/2013/150/abstr.html

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 $varphi(x(t),x(t-au))$ 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.