Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On the Order of Growth of Solutions to Complex Non-homogeneous Linear Differential Equations

  • Habib, Habib (Department of Mathematics, Laboratory of Biomathematics, University of Sidi Bel Abbes) ;
  • Belaidi, Benharrat (Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB))
  • Received : 2015.03.21
  • Accepted : 2016.07.29
  • Published : 2016.09.23
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Abstract

In this paper, we study the order of growth of solutions to the non-homogeneous linear differential equation $$f^{(k)}+A_{k-1}e^{az}f^{(k-1)}+{\cdots}+A_1e^{az}f^{\prime}+A_0e^{az}f=F_1e^{az}+F_2e^{bz}$$, where $A_j(z)$ (${\not\equiv}0$) ($j=0,1,{\cdots},k-1$), $F_j(z)$ (${\not\equiv}0$) (j = 1, 2) are entire functions and a, b are complex numbers such that $ab(a-b){\neq}0$.

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References

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