A second-order delay differential equation with multiple periodic solutions
The author considers the equation \[ x''(t)+ \omega^2x(t)= bx([t-1]),\tag{1} \] \(\omega\), \(b\) are real constants, \(b\neq 0\), \([\cdot]\) signifies the greatest integer function. The equation (1) is a differential equation with piecewise constant arguments and represents a hybrid of continuous and discrete dynamical systems. An existence of solutions to (1) is proved. It is shown that for certain values of the coefficieints, some or all of the solutions to (1) are monotone although the corresponding homogeneous equation is clearly oscillatory. For a specific relation between \(\omega\) and \(b\), there exist periodic solutions with different periods.
scientific article; zbMATH DE number 1251437
scientific article