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Cited by 48 publications
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References 19 publications
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“…Soon afterwards, such stability results of the differential equation y = λy in various abstract spaces have been obtained by Miura and Takahasi et al [12,13,22]. Since then, many interesting results on the Ulam stability of different types of differential equations have been established by various authors [1,3,4,5,7,8,9,10,11,14,15,17,18,19,20,21,23].…”
Section: Introductionmentioning
confidence: 87%
“…Soon afterwards, such stability results of the differential equation y = λy in various abstract spaces have been obtained by Miura and Takahasi et al [12,13,22]. Since then, many interesting results on the Ulam stability of different types of differential equations have been established by various authors [1,3,4,5,7,8,9,10,11,14,15,17,18,19,20,21,23].…”
Section: Introductionmentioning
confidence: 87%
“…Thereafter, Alsina and Ger published their paper [14], which handles the Hyers-Ulam stability of the linear differential equation y ′ (t) = y(t): If a differentiable function y(t) is a solution of the inequality |y ′ (t) − y(t)| ≤ ε for any t ∈ (a, ∞), then there exists a constant c such that |y(t) − ce t | ≤ 3ε for all t ∈ (a, ∞).Recently, the Hyers-Ulam stability problems of linear differential equations of first order and second order with constant coefficients were studied by using the method of integral factors (see [15,16]). The results given in [17][18][19] have been generalized by Popa and Rus [20,21] for the linear differential equations of nth order with constant coefficients. For more details on Hyers-Ulam stability and the generalized Hyers-Ulam stability, we refer the reader to the papers [22][23][24][25][26][27][28].…”
Section: Introductionmentioning
confidence: 99%
“…For some examples of differential equations which have the Hyers-Ulam stability on unbounded interval we refer the reader to [1,20,32,38], which show that it is a very special case that the Hyers-Ulam stability holds true for general differential equations on the whole domain.…”
Section: Introductionmentioning
confidence: 99%