Uniform global asymptotic stability for half-linear differential systems with time-varying coefficients

作者：Onitsuka Masakazu^*; Sugie Jitsuro

来源：Proceedings of the Royal Society of Edinburgh: Section A Mathematics , 2011, 141: 1083-1101.

where p and p* are positive numbers satisfying 1/p + 1/p* = 1, and phi(q)(z) = vertical bar z vertical bar(q-2)(z) for q = p or g = p*. This system is referred to as a half-linear system. We herein establish conditions on time-varying coefficients e(t), f(t), g(t) and h(t) for the zero solution to be uniformly globally asymptotically stable. If (e(t,), f(t)) equivalent to (h(t), g(t)), then the half-linear system is integrable. We consider two cases: the integrable case (e(t), f(t)) equivalent to (h(t), g(t)) and the non-integrable case (e(t), f(t)) not equivalent to (h(t), g(t)). Finally, some simple examples are presented to illustrate our results.

• 出版日期2011