Hyers–Ulam Stability of First Order Differential Equation via Integral Inequality

S. Tamilvanan (), E. Thandapani () and J. M. Rassias ()
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S. Tamilvanan: SRM Institute of Science and Technology, Department of Mathematics
E. Thandapani: University of Madras, Ramanujan Institute for Advanced Study in Mathematics
J. M. Rassias: National and Kapodistrian University of Athens, Pedagogical Department E.E., Section of Mathematics and Informatics

A chapter in Frontiers in Functional Equations and Analytic Inequalities, 2019, pp 153-158 from Springer

Abstract: Abstract In this chapter, first we derive a nonlinear integral inequality of Gollwitzer type, and as an application we investigate the Hyers–Ulam stability of nonlinear differential equation y ′ ( t ) = f ( t , y ( t ) ) , t ≥ a , $$\displaystyle y'(t) =f(t,y(t)),\, t\ge a , $$ where f is a given function. The obtained results are new to the literature.

Keywords: Hyers–Ulam stability; nonlinear differential equation; Gollwitzer type integral inequality; 34K10 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-28950-8_9

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DOI: 10.1007/978-3-030-28950-8_9

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