Asymptotic approximation of solutions of nonlinear third order difference equations
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AbstractIn this paper, we obtain asymptotic bounds, under appropriate conditions, of solutions of third order difference equations of the form $$ \Delta (p_{n - 1} \Delta (r_{n - 1} \Delta y_{n - 1} )) = f(n,y_n \Delta y_{n - 1} ) + g(n,y_n \Delta y_{n - 1} ), $$ where {p n} and {r n} are sequences of positive real numbers, and f, g: ℕ×ℝ2 → ℝ. Different forms of discrete Gronwall inequality are used to obtain these results.
2018 ◽
Vol 2018
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pp. 1-11
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2020 ◽
2009 ◽
Vol 2009
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pp. 1-11
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