On Zeros and Growth of Solutions of Second Order Linear Differential Equations
Commun. Korean Math. Soc.
Published online August 29, 2019
Sanjay Kumar and Manisha Saini
Deen Dayal Upadhyaya College, University of Delhi, University of Delhi
Abstract : For a second order linear differential equation $f''+A(z)f'+B(z)f=0$, with $ A(z)$ and $B(z)$ being transcendental entire functions under some restrictions, we have established that all non-trivial solutions are of infinite order. In addition, we have proved that these solutions, with a condition, have exponent of convergence of zeros equal to infinity. Also, we have extended these results to higher order linear differential equations.
Keywords : entire function, meromorphic function, order of growth, exponent of convergence, complex differential equation
MSC numbers : Primary 34M10, 30D35
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