Periodic solutions of second-order quasilinear hyperbolic equations

We study a periodic boundary-value problem for a quasilinear equation with the d'Alembert operator on the left-hand side and a nonlinear operator on the right-hand side and establish conditions under which the solution of the indicated problem is unique.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 10, pp. 1370–1375, October, 1995.     

Oleksii Mykolajovych Boholyubov (on His 90th Birthday)

Ukrainian Mathematical Journal -     

A class of nonlinear oscillational systems admitting exact solution of the Fokker-Planck-Kolmogorov equation

It is shown that the Fokker-Planck-Kolmogorov equation in amplitude and phase variables can be reduced to a first-order partial differential equation which admits exact integration for a large class of essentially nonlinear oscillational systems.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 10, pp. 1383–1388, October, 1991.