Unboundedness of solutions and instability of differential equations of the second order with delayed argument. (English) Zbl 1023.34061

The author investigates some asymptotic properties of the solutions to the equation \[ x''(t)+\sum_{i=1}^{n}p_i(t)x(t-\tau_i(t))=0,\quad p_i(t)\geq 0, \quad t\in[0,\infty),\quad x(\xi)=0\quad \text{for}\quad \xi<0. \tag{1} \] Several criteria for the existence of unbounded solutions to equation (1) are obtained. Also, tests of a Wronskian increase are acquired and a correlation between the growth of the Wronskian and the existence of unbounded solutions is established.


34K12 Growth, boundedness, comparison of solutions to functional-differential equations
34K20 Stability theory of functional-differential equations