Source method for nonautonomous systems (Q1079536)

The source method is extended to vector nonlinear differential equations \(\dot x=f(x,t),\quad t\in R,\quad x\in R^ n.\) The function \(f(x,t)\) is considered as the velocity field of an incompressible phase fluid, and its divergence is considered as the outflow of the sources of such fluid. The method is based on Liouville's integral formula for the divergence. Several solved examples of asymptotic unstability of low order time- variable nonlinear systems based on \(div f(x,t)\) are given.