In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic so...In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions.展开更多
Let A(z)be an entire function withμ(A)<1/2 such that the equation f^(k)+A(z)f=0,where k≥2,has a solution f with λ(f)<μ(A),and suppose that A1=A+h,where h■0 is an entire function with ρ(h)<μ(A).Then g^(...Let A(z)be an entire function withμ(A)<1/2 such that the equation f^(k)+A(z)f=0,where k≥2,has a solution f with λ(f)<μ(A),and suppose that A1=A+h,where h■0 is an entire function with ρ(h)<μ(A).Then g^(k)+A1(z)g=0 does not have a solution g with λ(g)<∞.展开更多
In this paper, we investigate the complex oscillation of the higher order differential equation where B0, ...,Bk-1,,F 0 are transcendental meromorpic functions having only finitely many poles. We obtain some precise e...In this paper, we investigate the complex oscillation of the higher order differential equation where B0, ...,Bk-1,,F 0 are transcendental meromorpic functions having only finitely many poles. We obtain some precise estimates of the exponent of convergence of the zero sequence of meromorphic solutions for the above equation.展开更多
In this paper, we investigate the complex oscillation of the non-homogeneous linear differential equation f(k)+Ak-1f(k-1)+… + A0f= F,where among A k-1,…A0, there exists one Ad being an entire function with infinite ...In this paper, we investigate the complex oscillation of the non-homogeneous linear differential equation f(k)+Ak-1f(k-1)+… + A0f= F,where among A k-1,…A0, there exists one Ad being an entire function with infinite order of growth, and the others Aj(j≠d) satisfy m(r,Aj) = 0{m(r,Ad)}, F≠0 is an entire function, and obtain some precise estimates of the exponent of convergence of the zero-sequence of its solutions.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
基金This work is supported by the National Natural Science Foundation of China (No.10161006)the Natural Science Foundation of Jiangxi Province (No.0311043).
文摘In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions.
基金This research is supported by the Research Foundation of Doctor Points of China （No. 20060422049） and the National Natural Science Foundation of China （No. 10371065）.
基金supported by the National Natural Science Foundation of China(Nos.11571049,11501142,11861023)the Foundation of Science and Technology project of Guizhou Province of China(No.[2018]5769-05).
文摘Let A(z)be an entire function withμ(A)<1/2 such that the equation f^(k)+A(z)f=0,where k≥2,has a solution f with λ(f)<μ(A),and suppose that A1=A+h,where h■0 is an entire function with ρ(h)<μ(A).Then g^(k)+A1(z)g=0 does not have a solution g with λ(g)<∞.
文摘In this paper, we investigate the complex oscillation of the higher order differential equation where B0, ...,Bk-1,,F 0 are transcendental meromorpic functions having only finitely many poles. We obtain some precise estimates of the exponent of convergence of the zero sequence of meromorphic solutions for the above equation.
文摘In this paper, we investigate the complex oscillation of the non-homogeneous linear differential equation f(k)+Ak-1f(k-1)+… + A0f= F,where among A k-1,…A0, there exists one Ad being an entire function with infinite order of growth, and the others Aj(j≠d) satisfy m(r,Aj) = 0{m(r,Ad)}, F≠0 is an entire function, and obtain some precise estimates of the exponent of convergence of the zero-sequence of its solutions.
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.
