This article investigates the property of linearly dependence of solutions f（z） and f（z ＋ 2πi） for higher order linear differential equations with entire periodic coefficients.
In this paper, we prove that, under appropriate hypotheses, the odd-order nonlinear neutral delay differential equation has the same oscillatory character as the associated linear equation with periodic coefficients O...In this paper, we prove that, under appropriate hypotheses, the odd-order nonlinear neutral delay differential equation has the same oscillatory character as the associated linear equation with periodic coefficients Our method is based on the establishment of a new comparison theorem for the oscillation of Eq.(E). Hence we prove that the parameter set such that Eq.(E) has a nonoscillatory solution is closed in certain metric space, and avoid the difficulty to set the necessary and sufficient condition for the oscillation of Eq.(E).展开更多
基金Supported by the Brain Pool Program of Korea Federation of Science and Technology Societies(072-1-3-0164)the Natural Science Foundation of Guangdong Province in China(06025059)
文摘This article investigates the property of linearly dependence of solutions f（z） and f（z ＋ 2πi） for higher order linear differential equations with entire periodic coefficients.
文摘In this paper, we prove that, under appropriate hypotheses, the odd-order nonlinear neutral delay differential equation has the same oscillatory character as the associated linear equation with periodic coefficients Our method is based on the establishment of a new comparison theorem for the oscillation of Eq.(E). Hence we prove that the parameter set such that Eq.(E) has a nonoscillatory solution is closed in certain metric space, and avoid the difficulty to set the necessary and sufficient condition for the oscillation of Eq.(E).
