CAJ | 학술논문

研究了如下代数微分方程a(z)f ′2+(b2(z)f2+b1(z)f+b 0(z))f ′=d3(z)f3+d2(z)f2+d1(z)f+d0(z)(这里a(z),bi(z)(0≤i≤2)和dj(z) (0≤j≤3)是多项式)超越整函数解的增长性,这类方程与有名的代数微分方程C(z,w)w′2+B(z,w)w′+A(z,w)=0(C(z,w)0, B(z,w)和A(z ,w)是z和w的3个多项式)有紧密的关系.详细地给出了第1个方程的整函数解的增长性与它的3个多项式的次数之间的关系.
연구료여하대수미분방정a(z)f ′2+(b2(z)f2+b1(z)f+b 0(z))f ′=d3(z)f3+d2(z)f2+d1(z)f+d0(z)(저리a(z),bi(z)(0≤i≤2)화dj(z) (0≤j≤3)시다항식)초월정함수해적증장성,저류방정여유명적대수미분방정C(z,w)w′2+B(z,w)w′+A(z,w)=0(C(z,w)0, B(z,w)화A(z ,w)시z화w적3개다항식)유긴밀적관계.상세지급출료제1개방정적정함수해적증장성여타적3개다항식적차수지간적관계.
In this paper, we investigate the growth of transcendental entire solutions of the following algebraic differential equation a(z)f ′2+(b 2(z)f2+b1(z)f+b0(z))f ′=d3(z)f3+d2(z)f2+d 1(z)f+d0(z), where a(z), bi(z) (0≤I≤2) and dj(z) (0≤j≤3) are all polynomials, and this equation relates closely to the following well -known algebraic differential equation C(z,w)w′2+B(z,w)w′+A(z,w)=0, where C(z,w)0, B(z,w) and A(z,w) are three polynomials in z and w. We give relationships between the growth of entire solutions and the degrees of the above three polynomials in detail.