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Implicit function theorem and its application to a Ulam’s problem for exact differential equations

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Abstract

We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g(x, y) + h(x, y)y′ = 0.

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Authors and Affiliations

  1. Mathematics Section, College of Science and Technology, Hong-Ik University, 339-701, Chochiwon, Republic of Korea

    Soon-Mo Jung

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  1. Soon-Mo Jung
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Correspondence to Soon-Mo Jung.

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Jung, SM. Implicit function theorem and its application to a Ulam’s problem for exact differential equations. Acta. Math. Sin.-English Ser. 26, 2085–2092 (2010). https://doi.org/10.1007/s10114-010-7611-z

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  • DOI: https://doi.org/10.1007/s10114-010-7611-z

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