Hyers-Ulam Stability of Euler's Equation in the Calculus of Variations

被引：5
|
作者：
Marian, Daniela [1 ]
Ciplea, Sorina Anamaria [2 ]
Lungu, Nicolaie [1 ]
机构：
[1] Tech Univ Cluj Napoca, Dept Math, 28 Memorandumului St, Cluj Napoca 400114, Romania
[2] Tech Univ Cluj Napoca, Dept Management & Technol, 28 Memorandumului St, Cluj Napoca 400114, Romania
来源：
MATHEMATICS | 2021年 / 9卷 / 24期
关键词：
Euler's equation; calculus of variations; Ulam-Hyers stability; Laplace transform; LINEAR-DIFFERENTIAL EQUATIONS; INTEGRAL-EQUATION; RASSIAS STABILITY; HIGHER-ORDER; 1ST-ORDER;
D O I：
10.3390/math9243320
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 & PRIME;) and when F=F(y,y & PRIME;). 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 Jyx-Jy0x 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.
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页数：9
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