A note for a second order periodic linear differential equation

In this paper, we study the characteristic exponent for a second order linear differential equation x ″ + q ( t ) x = 0 if q ( t ) < 0 . As an application, we calculate the characteristic exponents of Eq. x ″ + q ( t ) x = 0 when q ( t ) < 0 . The obtained results can be seen as a good generalization of Shi and coworkers [3,4]. We end this paper with some examples which show the simplicity and the high accuracy of our result.