Hyers–Ulam Stability of Order k for Euler Equation and Euler–Poisson Equation in the Calculus of Variations

Daniela Marian, Sorina Anamaria Ciplea and Nicolaie Lungu
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Daniela Marian: Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania
Sorina Anamaria Ciplea: Department of Management and Technology, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania
Nicolaie Lungu: Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania

Mathematics, 2022, vol. 10, issue 15, 1-9

Abstract: In this paper, we define and study Hyers–Ulam stability of order 1 for Euler’s equation and Hyers–Ulam stability of order m − 1 for the Euler–Poisson equation in the calculus of variations in two special cases, when these equations have the form y ″ ( x ) = f ( x ) and y ( m ) ( x ) = f ( x ) , respectively. We prove some estimations for J y x − J y 0 x , where y is an approximate solution and y 0 is an exact solution of the corresponding Euler and Euler-Poisson equations, respectively. We also give two examples.

Keywords: Euler equation; Euler–Poisson equation; calculus of variations; Hyers–Ulam stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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