Existence of Subharmonic Periodic Solutions to a Class of Second-Order Non-Autonomous Neutral Functional Differential Equations

By introducing subdifferentiability of lower semicontinuousconvex function φ(x(t),x(t−τ)) and its conjugate function, as wellas critical point theory and operator equation theory, we obtain the existence ofmultiple subharmonic periodic solutions to the following second-order nonlinearnonautonomous neutral nonlinear functional differential equation x″(t)+x″(t−2τ)+f(t,x(t),x(t−τ),x(t−2τ))=0, x(0)=0