The main purpose of this paper is to study the lower order and type of second order differential equation w"(z)-A(z)w=0,where A(z)is a polynomial.In the case of A(z)=a_dz^d,the authors prove that the lower order ...The main purpose of this paper is to study the lower order and type of second order differential equation w"(z)-A(z)w=0,where A(z)is a polynomial.In the case of A(z)=a_dz^d,the authors prove that the lower order and the type of all non-trivial solutions w of w"(z)-A(z)w=0 are equal to(d+2)/2 and(2(|a_d|)^(1/2))/(d+2)respectively.In the case of A(z)=a_dz^d+a_(d-1)z^(d-1)+…a_1z+a_0,a_d>0,a_(d-1)>0,…,a_1≥0,a_0≥0,the authors prove that the lower order of all non-trivial solutions w of w"(z)-A(z)w=0 is(d+2)/2.展开更多
基金Foundation item： Supported by the NNSF of China（11201395） Supported by the Science Foundation of Educational Commission of Hubei Province（Q20132801）
文摘The main purpose of this paper is to study the lower order and type of second order differential equation w"(z)-A(z)w=0,where A(z)is a polynomial.In the case of A(z)=a_dz^d,the authors prove that the lower order and the type of all non-trivial solutions w of w"(z)-A(z)w=0 are equal to(d+2)/2 and(2(|a_d|)^(1/2))/(d+2)respectively.In the case of A(z)=a_dz^d+a_(d-1)z^(d-1)+…a_1z+a_0,a_d>0,a_(d-1)>0,…,a_1≥0,a_0≥0,the authors prove that the lower order of all non-trivial solutions w of w"(z)-A(z)w=0 is(d+2)/2.
