Variational Integrals of a Class of Nonhomogeneous 𝒜-Harmonic Equations

Variational Integrals of a Class of Nonhomogeneous 𝒜-Harmonic Equations

We introduce a class of variational integrals whose Euler equations are nonhomogeneous 𝒜-harmonic equations. We investigate the relationship between the minimization problem and the Euler equation and give a simple proof of the existence of some nonhomogeneous 𝒜-harmonic equations by applying direct...

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Main Authors: Guanfeng Li, Yong Wang, Gejun Bao
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/697974
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spelling doaj-16584cbaee3f4a11abc84016ed3799852020-11-24T23:17:55ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/697974697974Variational Integrals of a Class of Nonhomogeneous 𝒜-Harmonic EquationsGuanfeng Li0Yong Wang1Gejun Bao2Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaWe introduce a class of variational integrals whose Euler equations are nonhomogeneous 𝒜-harmonic equations. We investigate the relationship between the minimization problem and the Euler equation and give a simple proof of the existence of some nonhomogeneous 𝒜-harmonic equations by applying direct methods of the calculus of variations. Besides, we establish some interesting results on variational integrals.http://dx.doi.org/10.1155/2014/697974
collection DOAJ
language English
format Article
sources DOAJ
author Guanfeng Li
Yong Wang
Gejun Bao
spellingShingle Guanfeng Li
Yong Wang
Gejun Bao
Variational Integrals of a Class of Nonhomogeneous 𝒜-Harmonic Equations
Abstract and Applied Analysis
author_facet Guanfeng Li
Yong Wang
Gejun Bao
author_sort Guanfeng Li
title Variational Integrals of a Class of Nonhomogeneous 𝒜-Harmonic Equations
title_short Variational Integrals of a Class of Nonhomogeneous 𝒜-Harmonic Equations
title_full Variational Integrals of a Class of Nonhomogeneous 𝒜-Harmonic Equations
title_fullStr Variational Integrals of a Class of Nonhomogeneous 𝒜-Harmonic Equations
title_full_unstemmed Variational Integrals of a Class of Nonhomogeneous 𝒜-Harmonic Equations
title_sort variational integrals of a class of nonhomogeneous 𝒜-harmonic equations
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description We introduce a class of variational integrals whose Euler equations are nonhomogeneous 𝒜-harmonic equations. We investigate the relationship between the minimization problem and the Euler equation and give a simple proof of the existence of some nonhomogeneous 𝒜-harmonic equations by applying direct methods of the calculus of variations. Besides, we establish some interesting results on variational integrals.
url http://dx.doi.org/10.1155/2014/697974
work_keys_str_mv AT guanfengli variationalintegralsofaclassofnonhomogeneousaharmonicequations
AT yongwang variationalintegralsofaclassofnonhomogeneousaharmonicequations
AT gejunbao variationalintegralsofaclassofnonhomogeneousaharmonicequations
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