Hyers-Ulam Stability of Euler’s 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, 2021, vol. 9, issue 24, 1-9

Abstract: In this paper we study Hyers-Ulam stability of Euler’s equation in the calculus of variations in two special cases: when F = F ( x , y ′ ) and when F = F ( y , y ′ ) . For the first case we use the direct method and for the second case we use the Laplace transform. In the first Theorem and in the first Example the corresponding estimations for J y x − J y 0 x are given. We mention that it is the first time that the problem of Ulam-stability of extremals for functionals represented in integral form is studied.

Keywords: Euler’s equation; calculus of variations; Ulam-Hyers stability; Laplace transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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