This paper investigates the growth of solutions of the equation f' + e -zf' + Q(z)f = 0 where the order (Q) = 1. When Q(z) = h(z)ebz, h(z) is nonzero polynomial, b ≠ -1 is a complex constant, every solution o...This paper investigates the growth of solutions of the equation f' + e -zf' + Q(z)f = 0 where the order (Q) = 1. When Q(z) = h(z)ebz, h(z) is nonzero polynomial, b ≠ -1 is a complex constant, every solution of the above equation has infinite order and the hyper-order 1. We improve the results of M. Frei, M. Ozawa, G. Gundersen and J. K. Langley.展开更多
In this paper, we investigate the growth and fixed points of solutions and their 1st, 2nd derivatives, differential polynomial of second order linear differential equations with meromorphic coefficients, and obtain th...In this paper, we investigate the growth and fixed points of solutions and their 1st, 2nd derivatives, differential polynomial of second order linear differential equations with meromorphic coefficients, and obtain that the exponents of convergence of these fixed points are all equal to the order of growth.展开更多
In this article, we study the complex oscillation problems of entire solutions to homogeneous and nonhomogeneous linear difference equations, and obtain some relations of the exponent of convergence of zeros and the o...In this article, we study the complex oscillation problems of entire solutions to homogeneous and nonhomogeneous linear difference equations, and obtain some relations of the exponent of convergence of zeros and the order of growth of entire solutions to complex linear difference equations.展开更多
In this paper, we investigate the complex oscillation of the differential equation f<sup>k</sup>+A<sub>k-1</sub>f<sup>k-1</sup>+…+A<sub>O</sub>f=F where A<sub>k-1...In this paper, we investigate the complex oscillation of the differential equation f<sup>k</sup>+A<sub>k-1</sub>f<sup>k-1</sup>+…+A<sub>O</sub>f=F where A<sub>k-1</sub>.…, A<sub>o</sub> F 0 are finite order transcendental entire functions, such that there exists an A<sub>d</sub>（0≤d≤k-1） being dominant in the sense that either it has larger order than any other A<sub>j</sub>（j=0.…. d-l. d+l.…. k-1）, or it is the only transcendental function. We obtain some precise estimates of the exponent of convergence of the zero-sequence of solutions to the above equation.展开更多
Under the conditions(without independence): (i) There Exists alpha > 0, such that sup E\Z(n)\(alpha) < +infinity, (ii) There Exists beta > 0, such that sup E\Z(n)\(-beta) < +infinity, the random series Sig...Under the conditions(without independence): (i) There Exists alpha > 0, such that sup E\Z(n)\(alpha) < +infinity, (ii) There Exists beta > 0, such that sup E\Z(n)\(-beta) < +infinity, the random series Sigma a(n) Z(n)e(-lambda n) and series' Sigma a(n)e(-lambda ns) a.s. have the same abscissa of convergence, the (R) order, lower order and type.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10161006) the Natural Science Foundation of Jiangxi Province.
文摘This paper investigates the growth of solutions of the equation f' + e -zf' + Q(z)f = 0 where the order (Q) = 1. When Q(z) = h(z)ebz, h(z) is nonzero polynomial, b ≠ -1 is a complex constant, every solution of the above equation has infinite order and the hyper-order 1. We improve the results of M. Frei, M. Ozawa, G. Gundersen and J. K. Langley.
基金the National Natural Science Foundation of China(No.10161006)the Natural Science Foundation of Guangdong Province in China(No.04010360)the Brain Pool Program of the Korean Federation of Science and Technology Societies(No.021-1-9)
文摘In this paper, we investigate the growth and fixed points of solutions and their 1st, 2nd derivatives, differential polynomial of second order linear differential equations with meromorphic coefficients, and obtain that the exponents of convergence of these fixed points are all equal to the order of growth.
基金supported by the National Natural Science Foundation of China (11171119 and 10871076)
文摘In this article, we study the complex oscillation problems of entire solutions to homogeneous and nonhomogeneous linear difference equations, and obtain some relations of the exponent of convergence of zeros and the order of growth of entire solutions to complex linear difference equations.
基金Project supported by the National Natural Science Foundation of China
文摘In this paper, we investigate the complex oscillation of the differential equation f<sup>k</sup>+A<sub>k-1</sub>f<sup>k-1</sup>+…+A<sub>O</sub>f=F where A<sub>k-1</sub>.…, A<sub>o</sub> F 0 are finite order transcendental entire functions, such that there exists an A<sub>d</sub>（0≤d≤k-1） being dominant in the sense that either it has larger order than any other A<sub>j</sub>（j=0.…. d-l. d+l.…. k-1）, or it is the only transcendental function. We obtain some precise estimates of the exponent of convergence of the zero-sequence of solutions to the above equation.
文摘Under the conditions(without independence): (i) There Exists alpha > 0, such that sup E\Z(n)\(alpha) < +infinity, (ii) There Exists beta > 0, such that sup E\Z(n)\(-beta) < +infinity, the random series Sigma a(n) Z(n)e(-lambda n) and series' Sigma a(n)e(-lambda ns) a.s. have the same abscissa of convergence, the (R) order, lower order and type.
