Eigenvalue problems for a quasilinear elliptic equation on ℝN
We prove the existence of a simple, isolated, positive principal eigenvalue for the quasilinear elliptic equation −Δpu=λg(x)|u|p−2u, x∈ℝN, lim|x|→+∞u(x)=0, where Δpu=div(|∇u|p−2∇u) is the p-Laplacian operator and the weight function g(x), being bounded, changes sign and is negative and away from zer...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.2871 |
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| _version_ | 1832551588359569408 |
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| author | Marilena N. Poulou Nikolaos M. Stavrakakis |
| author_facet | Marilena N. Poulou Nikolaos M. Stavrakakis |
| author_sort | Marilena N. Poulou |
| collection | DOAJ |
| description | We prove the existence of a simple, isolated, positive principal eigenvalue for the quasilinear elliptic equation −Δpu=λg(x)|u|p−2u, x∈ℝN, lim|x|→+∞u(x)=0, where Δpu=div(|∇u|p−2∇u) is the p-Laplacian operator and the weight function g(x), being bounded, changes sign and is negative and away from zero at infinity. |
| format | Article |
| id | doaj-art-17346dc4ceb94750894505c8757fff77 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-17346dc4ceb94750894505c8757fff772025-02-03T06:01:03ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005182871288210.1155/IJMMS.2005.2871Eigenvalue problems for a quasilinear elliptic equation on ℝNMarilena N. Poulou0Nikolaos M. Stavrakakis1Department of Mathematics, Faculty of Applied Mathematics and Physics, National Technical University of Athens, Zografou Campus, Athens 15780, GreeceDepartment of Mathematics, Faculty of Applied Mathematics and Physics, National Technical University of Athens, Zografou Campus, Athens 15780, GreeceWe prove the existence of a simple, isolated, positive principal eigenvalue for the quasilinear elliptic equation −Δpu=λg(x)|u|p−2u, x∈ℝN, lim|x|→+∞u(x)=0, where Δpu=div(|∇u|p−2∇u) is the p-Laplacian operator and the weight function g(x), being bounded, changes sign and is negative and away from zero at infinity.http://dx.doi.org/10.1155/IJMMS.2005.2871 |
| spellingShingle | Marilena N. Poulou Nikolaos M. Stavrakakis Eigenvalue problems for a quasilinear elliptic equation on ℝN International Journal of Mathematics and Mathematical Sciences |
| title | Eigenvalue problems for a quasilinear elliptic equation on ℝN |
| title_full | Eigenvalue problems for a quasilinear elliptic equation on ℝN |
| title_fullStr | Eigenvalue problems for a quasilinear elliptic equation on ℝN |
| title_full_unstemmed | Eigenvalue problems for a quasilinear elliptic equation on ℝN |
| title_short | Eigenvalue problems for a quasilinear elliptic equation on ℝN |
| title_sort | eigenvalue problems for a quasilinear elliptic equation on rn |
| url | http://dx.doi.org/10.1155/IJMMS.2005.2871 |
| work_keys_str_mv | AT marilenanpoulou eigenvalueproblemsforaquasilinearellipticequationonrn AT nikolaosmstavrakakis eigenvalueproblemsforaquasilinearellipticequationonrn |