Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations
We consider the problem −div(|∇u|p−2∇u)=a(x)(um+λun), x∈â„ÂN, N≥3, where 0<m<p−1<n,a(x)≥0, a(x) is not identically zero. Under the condition that a(x) satisfies (H), we show that there exists λ0>0 such that the above-mentioned equation...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2007-01-01
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| Series: | Boundary Value Problems |
| Online Access: | http://dx.doi.org/10.1155/2007/16407 |
| _version_ | 1811226750576754688 |
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| author | Zuodong Yang Bing Xu |
| author_facet | Zuodong Yang Bing Xu |
| author_sort | Zuodong Yang |
| collection | DOAJ |
| description | We consider the problem −div(|∇u|p−2∇u)=a(x)(um+λun), x∈â„ÂN, N≥3, where 0<m<p−1<n,a(x)≥0, a(x) is not identically zero. Under the condition that a(x) satisfies (H), we show that there exists λ0>0 such that the above-mentioned equation admits at least one solution for all λ∈(0,λ0). This extends the results of Laplace equation to the case of p-Laplace equation. |
| first_indexed | 2024-04-12T09:30:36Z |
| format | Article |
| id | doaj.art-b9ac7299d6524484868a8434211e8d79 |
| institution | Directory Open Access Journal |
| issn | 1687-2762 1687-2770 |
| language | English |
| last_indexed | 2024-04-12T09:30:36Z |
| publishDate | 2007-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-b9ac7299d6524484868a8434211e8d792022-12-22T03:38:22ZengSpringerOpenBoundary Value Problems1687-27621687-27702007-01-01200710.1155/2007/16407Entire Bounded Solutions for a Class of Quasilinear Elliptic EquationsZuodong YangBing XuWe consider the problem −div(|∇u|p−2∇u)=a(x)(um+λun), x∈â„ÂN, N≥3, where 0<m<p−1<n,a(x)≥0, a(x) is not identically zero. Under the condition that a(x) satisfies (H), we show that there exists λ0>0 such that the above-mentioned equation admits at least one solution for all λ∈(0,λ0). This extends the results of Laplace equation to the case of p-Laplace equation.http://dx.doi.org/10.1155/2007/16407 |
| spellingShingle | Zuodong Yang Bing Xu Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations Boundary Value Problems |
| title | Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations |
| title_full | Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations |
| title_fullStr | Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations |
| title_full_unstemmed | Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations |
| title_short | Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations |
| title_sort | entire bounded solutions for a class of quasilinear elliptic equations |
| url | http://dx.doi.org/10.1155/2007/16407 |
| work_keys_str_mv | AT zuodongyang entireboundedsolutionsforaclassofquasilinearellipticequations AT bingxu entireboundedsolutionsforaclassofquasilinearellipticequations |