Periodic solutions of a second-order functional differential equation with state-dependent argument
In this paper, a second order functional differential equation with state-dependent argument is considered: \[ c_0x''(t)+c_1x'(t) +c_2x(t) = x(p(t)+bx(t))+h(t), \] where \(c_i\) and \(b\) are nonzero constants and \(p\) and \(h\) are periodic functions with period \(T>0\). Under suitable assumptions and by using Schauder and Banach fixed point theorems, existence and uniqueness of a periodic solution is proved and continuous dependence of the periodic solution on \(p\) and \(h\) is shown to be valid.
scientific article; zbMATH DE number 6997091
scientific article