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

A. Javadian, E. Sorouri, G. H. Kim and M. Eshaghi Gordji

Journal of Applied Mathematics, 2011, vol. 2011, 1-10

Abstract:

We prove the generalized Hyers-Ulam stability of the 2nd-order linear differential equation of the form 𠑦 î…ž î…ž + ð ‘ ( ð ‘¥ ) 𠑦 î…ž + ð ‘ž ( ð ‘¥ ) 𠑦 = ð ‘“ ( ð ‘¥ ) , with condition that there exists a nonzero 𠑦 1 ∶ ð ¼ â†’ ð ‘‹ in ð ¶ 2 ( ð ¼ ) such that 𠑦 1 î…ž î…ž + ð ‘ ( ð ‘¥ ) 𠑦 î…ž 1 + ð ‘ž ( ð ‘¥ ) 𠑦 1 = 0 and ð ¼ 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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:813137

DOI: 10.1155/2011/813137

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