• 호남수학학술지
• /
• 제29권1호
• /
• pp.61-74
• /
• 2007

Th. M. Rassias obtained the Hyers-Ulam stability of the general Euler-Lagrange functional equation. In this paper we prove the stability of generlized Euler-Lagrange functional equations in the spirit of Hyers, Ulam, Rassias and G$\breve{a}$vruta.

• Korean Journal of Mathematics
• /
• 제30권4호
• /
• pp.571-592
• /
• 2022

By established a Banach space with the Hausdorff distance, we introduce the alternative fixed-point theorem to explore the existence and uniqueness of a fixed subset of Y and investigate the stability of set-valued Euler-Lagrange functional equations in this space. Some properties of the Hausdorff distance are furthermore explored by a short and simple way.

• Journal of applied mathematics & informatics
• /
• 제7권2호
• /
• pp.693-701
• /
• 2000

In this paper, we investigate a generalization of the Ulam stability problem of the 3-dimensional Euler-Lagrange functional equation f(x-y-z)+f(x)+f( y)+f(z)= f(x-y) +f(y+z) +f(z-x)

• 대한수학회논문집
• /
• 제16권4호
• /
• pp.607-619
• /
• 2001

Rassias obtained the Hyers-Ulam stability of the gen-eral Euler-Lagrange functional equation. In this paper we general-ized this stability in the spirit of Hyers, Ulam, Rassias and Gavruta.

• 대한수학회논문집
• /
• 제39권3호
• /
• pp.673-692
• /
• 2024

In this work, an alternative fashion of the multi-Jensen is introduced. The structures of the multi-Jensen and the multi-Euler-Lagrange-Jensen mappings are described. In other words, the system of n equations defining each of the mentioned mappings is unified as a single equation. Furthermore, by applying a fixed point theorem, the Hyers-Ulam stability for the multi-Euler-Lagrange-Jensen mappings in the setting of Banach spaces is established. An appropriate counterexample is supplied to invalidate the results in the case of singularity for multiadditive mappings.

• 대한토목학회논문집
• /
• 제29권5B호
• /
• pp.493-496
• /
• 2009

본 연구에서 Euler-Lagrange 식을 사용하여 속도포텐셜로 표현되는 확장형 완경사방정식을 유도하였다. 먼저, Euler-Lagrange 식을 사용하여 흐름함수로 표현된 확장형 완경사방정식을 유도한 Kim과 Bai(2004)의 유도과정을 따라가면서 속도 표텐셜로 표현된 확장형 완경사방정식과의 관계를 찾았다. 속도포텐셜로 표현된 Euler-Lagrange 식을 찾아낸 다음 고차의 수심변화 항을 유도하였다. 본 연구에서 유도된 확장형 완경사방정식은 기존의 식인 Massel(1993)의 식과 Chamberlain과 Porter(1995)의 식과 정확히 일치하였다. 본 연구의 연구 성과는 확장형 완경사방정식의 유도 방법을 새로 제시하여 해안공학의 영역을 넓히는데 의의가 있다.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1987년도 한국자동제어학술회의논문집; 한국과학기술대학, 충남; 16-17 Oct. 1987
• /
• pp.52-57
• /
• 1987

In this paper, it is dealt with the dynamic motion equations for a robot arm. Four kinds of the dynamic equations which are the Lagrange-Euler equations, the Recursive L-E equations, the Newton-Euler equations and the improved N-E equation are derived on robot PUMA 600. Finally the algorithms on these equations are programmed using PASCAL. and are compared with each other. As the results, it is found that the improved N-E equations has the most fastest execution time among the equations and can be used in real time processing.

• 한국해양공학회지
• /
• 제10권3호
• /
• pp.96-104
• /
• 1996

Hamilton's principle is used to derive Euler-Lagrange equations for free surface flow problems of incompressible ideal fluid. The velocity field is chosen to satisfy the continuity equation a priori. This approach results in a hierarchial set of governing equations consist of two evolution equations with respect to two canonical variables and corresponding boundary value problems. The free surface elevation and the Lagrange's multiplier are the canonical variables in Hamilton's sense. This Lagrange's multiplier is a velocity potential defined on the free surface. Energy is conserved as a consequence of the Hamiltonian structure. These equations can be applied to waves in water of finite depth including generalization of Hamilton's equations given by Miles and Salmon.

• 대한기계학회논문집
• /
• 제17권10호
• /
• pp.2457-2466
• /
• 1993

A simple method is presented for determining transient responses of locally nonlinear structures using substructure eigenproperties and Lagrange multiplier technique. Although the method is based upon the mode synthesis formulation procedure, the equations of the combined whole structure are not constructed compared with the conventional methods. Lagrange multi-pliers are used to enforce the conditions of geometric compatibility between the substructure interfaces and they are treated as external forces on each substructure itself. Substructure eigenvalue problem is defined with the substructure interface free of fixed. The transient analysis is based upon the recurrence discrete-time state equations and offers the simplicity of the Euler integration method without requiring small time increment and iterative solution procedure. Numerical examples reveal that the method is very accurated and efficient in calculating transient responses compared with the direct numerical integration method.

• Nonlinear Functional Analysis and Applications
• /
• 제28권4호
• /
• pp.865-876
• /
• 2023

This paper presents properties of the cocycle equations via cochains on a semigroup. And then we offer hyperstability results of related functional equations using the properties of cocycle equations via cochains. These results generalize hyperstability results of a class of linear functional equation by Maksa and Páles. The obtained results can be applied to obtain hyperstability of various functional equations such as Euler-Lagrange type quadratic equations.