Electron. J. Diff. Equ., Vol. 2013 (2013), No. 150, pp. 1-21.

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

Xiao-Bao Shu, Yongzeng Lai, Fei Xu

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.

Show me the PDF file (296 KB), TEX file, and other files for this article.

Xiao-Bao Shu
Department of Mathematics, Hunan University
Changsha 410082, China
email: sxb0221@163.com
Yongzeng Lai
Department of Mathematics, Wilfrid Laurier University
Waterloo, Ontario N2L 3C5, Canada
email: ylai@wlu.ca
Fei Xu
Department of Mathematics
Wilfrid Laurier University
Waterloo, Ontario N2L 3C5, Canada
email: fxu.feixu@gmail.com

Return to the EJDE web page