Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial conditions if any one of the coefficients is constant. Conclusions are then extended to include systems where both coefficients are time-varying.
Stability of Solutions to Damped Equations with Negative Stiffness
Existence of entire large and bounded solutions to a (k1,k2)-Hessian system with weights
Viewing nonoscillatory second order linear differential equations from the angle of Riccati equations
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