On zeros and growth of solutions of second order linear differential equations
Commun. Korean Math. Soc. 2020 Vol. 35, No. 1, 229-241
Published online January 31, 2020
Sanjay Kumar, Manisha Saini
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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