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 <i>x″(t) + p(t)xh(t) + f (t, (Tx)(t))</i> = 0, where <i>f</i> is a nonlinear function, <i>h(t)</i> is the lag of the argument, and <i>T</i> 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.