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On meromorphic solutions of differential equations with given poles
Lukivska Dzvenislava Volodymyrivna 1 , Shavala Olena 2
1 Department of theory of functions and functional analysis, Ivan Franko National University of Lviv, Lviv, 79000, Ukraine
2 GoIT, Kyiv, 01001, Ukraine
Keywords: meromorphic solutions, differential equations with given poles
Abstract

For a given sequence of complex numbers $Λ$ the equations $f^{(n)} + Af^m = 0,   m,n ∈ \mathbb{N} (f'' + Af = 0)$ were constructed, where $A$ is an entire (meromorphic in $\mathbb{C}$  ) function. This equations have meromorphic solutions with poles at the points of $Λ$. The result obtained for the equation $f'' + Af = 0$ is generalized for the case of two sequences.

References

[1] Šeda V. On some properties of solutions of the differential equation $y'' = Q(z)y,$ where $Q(z) \not\equiv 0$  is an entire function // Acta F.R.N. Univ. Comen. Mathem. - 1959. - 4 . - P. 223-253 (in Slovak).

[2]  Bank S. A note on the zero-sequences of solutions of linear differential equations // Results in Mathematics. - 1988. - 13 . - P. 1-11.

[3]  Shen L.-C. Construction of differential equation $y'' + Ay = 0$  with solutions having the prescribed zeros // Proceedings of the AMS. - 1985. - 95, N4. - P. 544-546.

[4]  Heittokangas J., Laine I. Solutions of $f'' + A(z)f = 0$  with prescribed sequences of zeros // Acta Math. Univ. Comenianae. - 2005. - 74 , N2. - P. 287- 307.

[5]  Bank S., Laine I. On the zeros of meromorphic solutions of second-order linear differential equations // Comment. Math. Helvetici. - 1983. - 58 , N1. - P. 656-677.

[6] Kudryashov N. A. Nonlinear differential equations of the fourth order with transcendental solutions // Theoretical and Mathematical Physics.  2000. 122, N1.  P. 72-87.

[7] Kudryashov N. A. Generalizations of the Penlevé equations // Theoretical and Mathematical Physics. 2003. 137, N3.  P. 408-423.

[8] Shabat B. V. Introduction to complex analysis. M.: Nauka, 1976.  320 p.

[9]  Eremenko A., Liao L., Ng T. Meromorphic solutions of higher order Briot-Bouquet differential equations // Math. Proc. Camb. Phil. Soc. - 2009. - 146 . - P. 197-206.

Cite
ACS Style
Lukivska, .V.; Shavala, O. On meromorphic solutions of differential equations with given poles. Bukovinian Mathematical Journal. 2016, 3
AMA Style
Lukivska V, Shavala O. On meromorphic solutions of differential equations with given poles. Bukovinian Mathematical Journal. 2016; 3(2).
Chicago/Turabian Style
Dzvenislava Volodymyrivna Lukivska, Olena Shavala. 2016. "On meromorphic solutions of differential equations with given poles". Bukovinian Mathematical Journal. 3 no. 2.
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