On Semiaxis Boundness of the Solution of Nonlinear Differential Equation of Second Order Delay
The paper examines the problem of limitation on the semi-axis solutions of functionaldifferential equation x″(t) + p(t)xh(t) + f (t, (Tx)(t)) = 0, where f is a nonlinear function, h(t) is the lag of the argument, and T is a bounded linear operator. Under certain conditions on the nonlinearity and the lag of the argument, we prove the boundedness on a semi-axis of solutions for such equations.