The paper is devoted to non-homogeneous second-order differential equations with polynomial right parts and polynomial coefficients.We derive estimates for the partial sums and products of the zeros of solutions to th...The paper is devoted to non-homogeneous second-order differential equations with polynomial right parts and polynomial coefficients.We derive estimates for the partial sums and products of the zeros of solutions to the considered equations.These estimates give us bounds for the function counting the zeros of solutions and information about the zero-free domains.展开更多
Suppose that B is a rational function having a pole at co of order n ＞ 0 and that H 0 is a meromorphic function satisfying o(H) =β (n+ k)/k. If the differential equation f(k) + Bf =H(z) has a meromorphic solution f,...Suppose that B is a rational function having a pole at co of order n ＞ 0 and that H 0 is a meromorphic function satisfying o(H) =β (n+ k)/k. If the differential equation f(k) + Bf =H(z) has a meromorphic solution f, then all meromorphic solutions f satisfy λ(f) = λ(f) = δ(f) = max{β, (n + k)/k},except at most one exceptional meromorphic solution f0.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
文摘The paper is devoted to non-homogeneous second-order differential equations with polynomial right parts and polynomial coefficients.We derive estimates for the partial sums and products of the zeros of solutions to the considered equations.These estimates give us bounds for the function counting the zeros of solutions and information about the zero-free domains.
文摘Suppose that B is a rational function having a pole at co of order n ＞ 0 and that H 0 is a meromorphic function satisfying o(H) =β (n+ k)/k. If the differential equation f(k) + Bf =H(z) has a meromorphic solution f, then all meromorphic solutions f satisfy λ(f) = λ(f) = δ(f) = max{β, (n + k)/k},except at most one exceptional meromorphic solution f0.
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.
