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Existence of a solution of discrete Emden-Fowler equation caused by continuous equation

  • * Corresponding author: Josef Diblík

    * Corresponding author: Josef Diblík 
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  • The paper studies the asymptotic behaviour of solutions to a second-order non-linear discrete equation of Emden–Fowler type

    $ \Delta^2 u(k) \pm k^\alpha u^m(k) = 0 $

    where $ u\colon \{k_0, k_0+1, \dots\}\to \mathbb{R} $ is an unknown solution, $ \Delta^2 u(k) $ is its second-order forward difference, $ k_0 $ is a fixed integer and $ \alpha $, $ m $ are real numbers, $ m\not = 0, 1 $.

    Mathematics Subject Classification: Primary: 39A33, 39A22; Secondary: 39A12.

    Citation:

    \begin{equation} \\ \end{equation}
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  • Figure 1.  Solution of the system (69)

    Figure 2.  Solution of the system (70), (71)

    Figure 3.  Solution of the system (73)

    Figure 4.  Solution of the system (74)

    Figure 5.  Summary of admissible values

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