A necessary and sufficient condition for the global asymptotic stability of damped half-linear oscillators

作者：Hata S; Sugie J^*

来源：Acta Mathematica Hungarica, 2013, 138(1-2): 156-172.

DOI：10.1007/s10474-012-0259-7

• global asymptotic stability
• half-linear differential equation
• damped oscillator
• growth condition
• Prufer transformation
• Riccati transformation

We are concerned with the global asymptotic stability of the equilibrium of the half-linear differential equation with a damped term %26lt;br%26gt;(phi(p)(x%26apos;))%26apos; + h(t)phi(p)(x%26apos;) + (p - 1)phi(p)(x) = 0. %26lt;br%26gt;A necessary and sufficient growth condition on h(t) is obtained by using the generalized Prufer transformation and the generalized Riccati transformation. Equivalent planar systems to the above-mentioned equation are also considered in the proof of our main result.

• 出版日期2013-1