Some Properties of Approximate Solutions of Linear Differential Equations
作者： Ginkyu Choi Soon-Mo Choi , Jaiok Jung , Roh
DOI: 10.3390/MATH7090806
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摘要: In this paper, we will consider the Hyers-Ulam stability for second order inhomogeneous linear differential equation, u ″ ( x ) + α ′ β = r , with constant coefficients. More precisely, study properties of approximate solutions above equation in class twice continuously differentiable functions suitable conditions and compare them homogeneous 0 . Several mathematicians have studied such they obtained good results. use classical integral method, via Wronskian, to establish coefficients our result previous ones. Specially, any desired point c ∈ R can a solution near very small error estimation.
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sci-hub.se 参考文章(13)
Soon-Mo Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis ,(2011)
Claudi Alsina, Roman Ger, On Some Inequalities and Stability Results Related to the Exponential Function Journal of Inequalities and Applications. ,vol. 1998, pp. 246904- ,(1998) , 10.1155/S102558349800023X
Dorian Popa, Ioan Raşa, Hyers–Ulam stability of the linear differential operator with nonconstant coefficients Applied Mathematics and Computation. ,vol. 219, pp. 1562- 1568 ,(2012) , 10.1016/J.AMC.2012.07.056
Sin-Ei Takahasi, Takeshi Miura, Shizuo Miyajima, ON THE HYERS-ULAM STABILITY OF THE BANACH SPACE-VALUED DIFFERENTIAL EQUATION y'=λy Bulletin of the Korean Mathematical Society. ,vol. 39, pp. 309- 315 ,(2002) , 10.4134/BKMS.2002.39.2.309
Dorian Popa, Ioan Raşa, On the Hyers–Ulam stability of the linear differential equation Journal of Mathematical Analysis and Applications. ,vol. 381, pp. 530- 537 ,(2011) , 10.1016/J.JMAA.2011.02.051
Dalia Sabina Cîmpean, Dorian Popa, On the stability of the linear differential equation of higher order with constant coefficients Applied Mathematics and Computation. ,vol. 217, pp. 4141- 4146 ,(2010) , 10.1016/J.AMC.2010.09.062
Hamid Rezaei, Soon-Mo Jung, Themistocles M. Rassias, Laplace transform and Hyers–Ulam stability of linear differential equations Journal of Mathematical Analysis and Applications. ,vol. 403, pp. 244- 251 ,(2013) , 10.1016/J.JMAA.2013.02.034
Yongjin Li, Yan Shen, Hyers–Ulam stability of linear differential equations of second order Applied Mathematics Letters. ,vol. 23, pp. 306- 309 ,(2010) , 10.1016/J.AML.2009.09.020
Soon-Mo Jung, Hyers–Ulam stability of a system of first order linear differential equations with constant coefficients☆ Journal of Mathematical Analysis and Applications. ,vol. 320, pp. 549- 561 ,(2006) , 10.1016/J.JMAA.2005.07.032
Yongjin Li, Yan Shen, Hyers-Ulam Stability of Nonhomogeneous Linear Differential Equations of Second Order International Journal of Mathematics and Mathematical Sciences. ,vol. 2009, pp. 1- 7 ,(2009) , 10.1155/2009/576852