In this paper, we investigate the growth of transcendental entire solutionsof the following algebraic differential equation a(z)f'~2 +(b_2(z)f^2 +b_1(z)f +b_0(z))f'=d_3(z)f^3+d_2(z)f^2 +d_1(z)f +d_0(z), where ...In this paper, we investigate the growth of transcendental entire solutionsof the following algebraic differential equation a(z)f'~2 +(b_2(z)f^2 +b_1(z)f +b_0(z))f'=d_3(z)f^3+d_2(z)f^2 +d_1(z)f +d_0(z), where a(z), b_i(z) (0<- i <=2) and d_j (z) (0<=j<= 3) are allpolynomials, and this equation relates closely to the following well-known algebraic differentialequation C(z,w)w'~2 + B(z,w)w' + A(z,w) =0, where G(z,w)not ident to 0, B(z,w) and A(z,w) are threepolynomials in z and w. We give relationships between the growth of entire solutions and the degreesof the above three polynomials in detail.展开更多
In this paper, we study the deficient relation of some transcendental entire functions. If f j(z)(j=1,2,...,p) be transcendental entire functions, and let a j(j=1,2,...,p) be nonzero finite complex numbers....In this paper, we study the deficient relation of some transcendental entire functions. If f j(z)(j=1,2,...,p) be transcendental entire functions, and let a j(j=1,2,...,p) be nonzero finite complex numbers. If ∑pj=1a jf j(z)≡1 , then ∑pj=1δ p-1 (0,f j)≤p-1, where δ p-1 (0,f j)=1- lim r→∞N p-1 (r,1/f j)T(r,f j) (j=1,2,...,p). The result improves a result of Niino and Ozawa. Meanwhile we give some applications of our result.展开更多
文摘In this paper, we investigate the growth of transcendental entire solutionsof the following algebraic differential equation a(z)f'~2 +(b_2(z)f^2 +b_1(z)f +b_0(z))f'=d_3(z)f^3+d_2(z)f^2 +d_1(z)f +d_0(z), where a(z), b_i(z) (0<- i <=2) and d_j (z) (0<=j<= 3) are allpolynomials, and this equation relates closely to the following well-known algebraic differentialequation C(z,w)w'~2 + B(z,w)w' + A(z,w) =0, where G(z,w)not ident to 0, B(z,w) and A(z,w) are threepolynomials in z and w. We give relationships between the growth of entire solutions and the degreesof the above three polynomials in detail.
文摘In this paper, we study the deficient relation of some transcendental entire functions. If f j(z)(j=1,2,...,p) be transcendental entire functions, and let a j(j=1,2,...,p) be nonzero finite complex numbers. If ∑pj=1a jf j(z)≡1 , then ∑pj=1δ p-1 (0,f j)≤p-1, where δ p-1 (0,f j)=1- lim r→∞N p-1 (r,1/f j)T(r,f j) (j=1,2,...,p). The result improves a result of Niino and Ozawa. Meanwhile we give some applications of our result.
