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

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

Keywords

• Subharmonic periodic solution
• variational structure
• operator equation
• critical point
• subdifferential
• neutral functional differential equation
• Z2-group
• index theory