In this paper we obtain some Ulam stability results for the second order and the third order linear difference equation with nonconstant coefficients in a Banach space. The main idea of the approach is to decompose the second order linear difference equation in a Riccati difference equation and a first order difference equation. In this way we extend some results for linear difference equations with constant coefficients and for linear difference equations with periodic coefficients.
Citation: Delia-Maria Kerekes, Bianca Moșneguțu, Dorian Popa. On Ulam stability of a second order linear difference equation[J]. AIMS Mathematics, 2023, 8(9): 20254-20268. doi: 10.3934/math.20231032
In this paper we obtain some Ulam stability results for the second order and the third order linear difference equation with nonconstant coefficients in a Banach space. The main idea of the approach is to decompose the second order linear difference equation in a Riccati difference equation and a first order difference equation. In this way we extend some results for linear difference equations with constant coefficients and for linear difference equations with periodic coefficients.
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Delia-Maria Kerekes, Bianca Moșneguțu, Dorian Popa. On Ulam stability of a second order linear difference equation[J]. AIMS Mathematics, 2023, 8(9): 20254-20268. doi: 10.3934/math.20231032
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