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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/697974 |
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| _version_ | 1832564521083863040 |
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| author | Guanfeng Li Yong Wang Gejun Bao |
| author_facet | Guanfeng Li Yong Wang Gejun Bao |
| author_sort | Guanfeng Li |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-16584cbaee3f4a11abc84016ed379985 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-16584cbaee3f4a11abc84016ed3799852025-02-03T01:10:46ZengWileyAbstract 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 |
| spellingShingle | Guanfeng Li Yong Wang Gejun Bao Variational Integrals of a Class of Nonhomogeneous 𝒜-Harmonic Equations Abstract and Applied Analysis |
| title | 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_short | Variational Integrals of a Class of Nonhomogeneous 𝒜-Harmonic Equations |
| title_sort | variational integrals of a class of nonhomogeneous 𝒜 harmonic equations |
| url | http://dx.doi.org/10.1155/2014/697974 |
| work_keys_str_mv | AT guanfengli variationalintegralsofaclassofnonhomogeneousaharmonicequations AT yongwang variationalintegralsofaclassofnonhomogeneousaharmonicequations AT gejunbao variationalintegralsofaclassofnonhomogeneousaharmonicequations |