Parametric nonoscillation region is given for the Mathieu-type differential equation
where α and β are real parameters. Oscillation problem about a kind of Meissner’s equation is also discussed. The obtained result is proved by using Sturm’s comparison theorem and phase plane analysis of the second-order differential equation
where a, b:[0,∞)→R are continuous functions. The feature of the result is the ease of chequing whether the obtained condition is satisfied or not. Parametric nonoscilla- tion region about (α,β) and some solution orbits are drawn to help understand the result.
Parametric nonoscillation region
Damped linear differential equations
Phase plane analysis
Monatshefte für Mathematik
Faculty of Science and Engineering