Existence and Multiplicity of Positive Solutions to a Class of Quasilinear Elliptic Equations in ℝN
We consider the following class of quasilinear elliptic equations -hpΔpu+Vε(x)|u|p-2u=|u|q-2u, u(x)>0 for all x∈RN, where h>0, Δpu= div(|∇u|p-2∇u), 2≤p<N, p<q�...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2010-01-01
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| Series: | Boundary Value Problems |
| Online Access: | http://dx.doi.org/10.1155/2010/579387 |
| _version_ | 1818355492365271040 |
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| author | Tsing-San Hsu |
| author_facet | Tsing-San Hsu |
| author_sort | Tsing-San Hsu |
| collection | DOAJ |
| description | We consider the following class of quasilinear elliptic equations -hpΔpu+Vε(x)|u|p-2u=|u|q-2u, u(x)>0 for all x∈RN, where h>0, Δpu= div(|∇u|p-2∇u), 2≤p<N, p<q<p*=Np/(N-p). We allow the potential Vε to be unbounded below and prove the existence and multiplicity for positive solutions. |
| first_indexed | 2024-12-13T19:42:11Z |
| format | Article |
| id | doaj.art-c6fdcca0fee54186a67bb193c1d7e22d |
| institution | Directory Open Access Journal |
| issn | 1687-2762 1687-2770 |
| language | English |
| last_indexed | 2024-12-13T19:42:11Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-c6fdcca0fee54186a67bb193c1d7e22d2022-12-21T23:33:40ZengSpringerOpenBoundary Value Problems1687-27621687-27702010-01-01201010.1155/2010/579387Existence and Multiplicity of Positive Solutions to a Class of Quasilinear Elliptic Equations in ℝNTsing-San HsuWe consider the following class of quasilinear elliptic equations -hpΔpu+Vε(x)|u|p-2u=|u|q-2u, u(x)>0 for all x∈RN, where h>0, Δpu= div(|∇u|p-2∇u), 2≤p<N, p<q<p*=Np/(N-p). We allow the potential Vε to be unbounded below and prove the existence and multiplicity for positive solutions.http://dx.doi.org/10.1155/2010/579387 |
| spellingShingle | Tsing-San Hsu Existence and Multiplicity of Positive Solutions to a Class of Quasilinear Elliptic Equations in ℝN Boundary Value Problems |
| title | Existence and Multiplicity of Positive Solutions to a Class of Quasilinear Elliptic Equations in ℝN |
| title_full | Existence and Multiplicity of Positive Solutions to a Class of Quasilinear Elliptic Equations in ℝN |
| title_fullStr | Existence and Multiplicity of Positive Solutions to a Class of Quasilinear Elliptic Equations in ℝN |
| title_full_unstemmed | Existence and Multiplicity of Positive Solutions to a Class of Quasilinear Elliptic Equations in ℝN |
| title_short | Existence and Multiplicity of Positive Solutions to a Class of Quasilinear Elliptic Equations in ℝN |
| title_sort | existence and multiplicity of positive solutions to a class of quasilinear elliptic equations in x211d n |
| url | http://dx.doi.org/10.1155/2010/579387 |
| work_keys_str_mv | AT tsingsanhsu existenceandmultiplicityofpositivesolutionstoaclassofquasilinearellipticequationsinx211dn |