Let f and g be two permutable transcendental entire functions. In this paper, we first prove that J(fg)=J(f n g m) for any positive integers n and m . Then we prove that the function h(p(z))+az ∈/ B , where h(z) is...Let f and g be two permutable transcendental entire functions. In this paper, we first prove that J(fg)=J(f n g m) for any positive integers n and m . Then we prove that the function h(p(z))+az ∈/ B , where h(z) is any transcendental entire function with h′(z)=0 having infinitely many solutions, p(z) is a polynomial with deg p ≥2 and a(≠0) ∈ C .展开更多
Some results of existence of positive solutions for singular boundary value problems{-u″(t) = p(t)f(u(t)), t ∈ (0, 1),u(0) = u(1) = 0are given, where the function p(t) may be singular at t = 0,1.
文摘Let f and g be two permutable transcendental entire functions. In this paper, we first prove that J(fg)=J(f n g m) for any positive integers n and m . Then we prove that the function h(p(z))+az ∈/ B , where h(z) is any transcendental entire function with h′(z)=0 having infinitely many solutions, p(z) is a polynomial with deg p ≥2 and a(≠0) ∈ C .
基金Project supported by the 973 Project of the Ministry of Science and Technology of China (No.G1999075109)
文摘Some results of existence of positive solutions for singular boundary value problems{-u″(t) = p(t)f(u(t)), t ∈ (0, 1),u(0) = u(1) = 0are given, where the function p(t) may be singular at t = 0,1.
