On the periodic solutions of a forced second-order equation
A two-dimensional irrotational forced shallow water sloshing model leads in the case of periodic solutions to a second-order nonlinear nonautonomous ordinary differential equation. Shooting technique resembling that used previously for the Falkner-Skan equation is applied. The existence of many harmonic and subharmonic solutions is rigorously proved confirming previously found (4th order Runge-Kutta) numerical solutions. A ``Kneading'' theory is obtained for the ordering of the initial conditions according to the pattern of ``spikes'' exhibited by the solution.
two-dimensional irrotational forced shallow water sloshing model
second-order nonlinear nonautonomous ordinary differential equation
scientific article; zbMATH DE number 563418