Generalized Hyers-Ulam Stability of the Second-Order Linear Differential Equations

Generalized Hyers-Ulam Stability of the Second-Order Linear Differential Equations

We prove the generalized Hyers-Ulam stability of the 2nd-order linear differential equation of the form y′′+p(x)y′+q(x)y=f(x), with condition that there exists a nonzero y1:I→X in C2(I) such that y1′′+p(x)y1′+q(x)y1=0 and I is an open interval. As a consequence of our main theorem, we prove the gene...

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Veröffentlicht in:Journal of Applied Mathematics 2011-01, Vol.2011 (1), p.1730-1739-103
Hauptverfasser: Javadian, A., Sorouri, E., Kim, G. H., Gordji, M. Eshaghi
Format: Artikel
Sprache:eng
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Zusammenfassung:We prove the generalized Hyers-Ulam stability of the 2nd-order linear differential equation of the form y′′+p(x)y′+q(x)y=f(x), with condition that there exists a nonzero y1:I→X in C2(I) such that y1′′+p(x)y1′+q(x)y1=0 and I is an open interval. As a consequence of our main theorem, we prove the generalized Hyers-Ulam stability of several important well-known differential equations.
ISSN:1110-757X
1687-0042
DOI:10.1155/2011/813137