Geodesic
Sums of zeros of solutions to second order ODE with non-polynomial coefficients
Electronic journal of differential equations, Tome 2012 (2012)
We consider the equation

$ |F(z)|\le A \exp \big(\frac{|z|^\rho}{\rho}\big)\quad (\rho\ge 1,\; A=hbox{const}>0). $

Let

$ \sum_{k=1}^j \frac{1}{|z_k(y)|} \quad (j=1, 2, \dots) $

are established. Some applications of these bounds are also considered.
Classification : 34C10, 34A30
Keywords: complex differential equation, zeros of solutions 
@article{EJDE_2012__2012__a81,
     author = {Gil',  Michael I.},
     title = {Sums of zeros of solutions to second order {ODE} with non-polynomial coefficients},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1260.34162},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a81/}
}
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%A Gil',  Michael I.
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%J Electronic journal of differential equations
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Gil',  Michael I. Sums of zeros of solutions to second order ODE with non-polynomial coefficients. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a81/