arXiv subjects
Publications and source records attributed to S. K. Chanyal.
In this article, we study about the solutions of second order linear differential equations by considering several conditions on the coefficients of homogenous linear differential equation and its associated non-homogenous linear differential equation.
This article is devoted to the study of solutions of non-homogenous linear differential equations having entire coefficients. We get all non-trivial solutions of infinite order of equation $f^{(n)}+a_{n-1}(z)f^{(n-1)}+\ldots +a_1f'+a_0f=H(z)$, by restricting the conditions on coefficients.
In this study, we show that all non-trivial solutions of $f"+A(z)f'+B(z)f=0$ have infinite order, provided that the entire coefficient $A(z)$ has certain restrictions and $B(z)$ has multiply-connected Fatou component. We also extend these results to higher order linear differential equations.
This article contains the theorems which shows that when $A(z)=h_1(z)e^{P_1(z)}$ and $B(z)=h_0(z)e^{P_0(z)}$ are of same order,then all the non-trivial solutions of equation $f"+A(z)f'+B(z)f=0$ are of infinite order. Moreover we extend these results to higher order differential equations.