On The Oscillation Results Of Solutions Of Some Linear Differential Equations

In this dissertation,we investigate the oscillation results of solutions of some linear differential equations.The growth of order and the exponent of convergence of zeros are studied for linear differential equations.The main novelties and results are briefly stated below.1.In Chapter three,the distribution of zeros of solutions of higher order of the linear differential equation y(k+∑Ajy(j)=0investigated by using complex oscillation theory of linear differential equations.It is proved that the exponent of convergence of zeros of every transcendental solution of the equation is infinite if given a small perturbation to one of the coefficients.2.In Chapter four we study the growth of order of solutions of the linear differential equation f(k)+Ak-1f(k-1)+…+Asf(s)+…+A1f’+A0f=0.Under some hypothesis,we obtain that the order of each solution for such equation is infinite.3.In Chapter five,we investigate the growth of order and hyper order of solutions of f"fe-zn f’+(A1eP(z)+A2eQ(z))f=0.By using Nevanlinna theory and complex oscill ation theory of differential equations,we obtain the precise estimates of growth of order and hyper order of solutions of such equation.