Existence of Solutions for Nonhomogeneous A-Harmonic Equations with Variable Growth
We study the following nonhomogeneous A-harmonic equations: d*A(x,du(x))+B(x,u(x))=0, x∈Ω, u(x)=0, x∈∂Ω, where Ω⊂ℝn is a bounded and convex Lipschitz domain, A(x,du(x)) and B(x,u(x)) satisfy some p(x)-growth conditions, respectively. We obtain the existence of weak solutions for the above equat...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/421571 |
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| author | Yongqiang Fu Lifeng Guo |
| author_facet | Yongqiang Fu Lifeng Guo |
| author_sort | Yongqiang Fu |
| collection | DOAJ |
| description | We study the following nonhomogeneous A-harmonic equations: d*A(x,du(x))+B(x,u(x))=0, x∈Ω, u(x)=0, x∈∂Ω, where Ω⊂ℝn is a bounded and convex Lipschitz domain, A(x,du(x)) and B(x,u(x)) satisfy some p(x)-growth conditions, respectively. We obtain the existence of weak solutions for the above equations in subspace 𝔎01,p(x)(Ω,Λl-1) of W01,p(x)(Ω,Λl-1). |
| format | Article |
| id | doaj-art-67c92ed3f9d44583879c6469962e3374 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-67c92ed3f9d44583879c6469962e33742025-02-03T01:25:03ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/421571421571Existence of Solutions for Nonhomogeneous A-Harmonic Equations with Variable GrowthYongqiang Fu0Lifeng Guo1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaWe study the following nonhomogeneous A-harmonic equations: d*A(x,du(x))+B(x,u(x))=0, x∈Ω, u(x)=0, x∈∂Ω, where Ω⊂ℝn is a bounded and convex Lipschitz domain, A(x,du(x)) and B(x,u(x)) satisfy some p(x)-growth conditions, respectively. We obtain the existence of weak solutions for the above equations in subspace 𝔎01,p(x)(Ω,Λl-1) of W01,p(x)(Ω,Λl-1).http://dx.doi.org/10.1155/2012/421571 |
| spellingShingle | Yongqiang Fu Lifeng Guo Existence of Solutions for Nonhomogeneous A-Harmonic Equations with Variable Growth Abstract and Applied Analysis |
| title | Existence of Solutions for Nonhomogeneous A-Harmonic Equations with Variable Growth |
| title_full | Existence of Solutions for Nonhomogeneous A-Harmonic Equations with Variable Growth |
| title_fullStr | Existence of Solutions for Nonhomogeneous A-Harmonic Equations with Variable Growth |
| title_full_unstemmed | Existence of Solutions for Nonhomogeneous A-Harmonic Equations with Variable Growth |
| title_short | Existence of Solutions for Nonhomogeneous A-Harmonic Equations with Variable Growth |
| title_sort | existence of solutions for nonhomogeneous a harmonic equations with variable growth |
| url | http://dx.doi.org/10.1155/2012/421571 |
| work_keys_str_mv | AT yongqiangfu existenceofsolutionsfornonhomogeneousaharmonicequationswithvariablegrowth AT lifengguo existenceofsolutionsfornonhomogeneousaharmonicequationswithvariablegrowth |