Multiple Solutions of Quasilinear Elliptic Equations in ℝ𝑁
Assume that 𝑄 is a positive continuous function in ℝ𝑁 and satisfies some suitable conditions. We prove that the quasilinear elliptic equation −Δ𝑝𝑢+|𝑢|𝑝−2𝑢=𝑄(𝑧)|𝑢|𝑞−2𝑢 in ℝ𝑁 admits at least two solutions in ℝ𝑁 (one is a positive ground-state solution and the other is a sign-changing solution)....
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2010/673526 |
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| _version_ | 1850163149202784256 |
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| author | Huei-li Lin |
| author_facet | Huei-li Lin |
| author_sort | Huei-li Lin |
| collection | DOAJ |
| description | Assume that 𝑄 is a positive continuous function in ℝ𝑁 and satisfies some suitable conditions. We prove that the quasilinear elliptic equation −Δ𝑝𝑢+|𝑢|𝑝−2𝑢=𝑄(𝑧)|𝑢|𝑞−2𝑢 in ℝ𝑁 admits at least two solutions in ℝ𝑁 (one is a positive ground-state solution and the other is a sign-changing solution). |
| format | Article |
| id | doaj-art-ef063bf03a97468994ba484d87a6a524 |
| institution | OA Journals |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-ef063bf03a97468994ba484d87a6a5242025-08-20T02:22:21ZengWileyInternational Journal of Differential Equations1687-96431687-96512010-01-01201010.1155/2010/673526673526Multiple Solutions of Quasilinear Elliptic Equations in ℝ𝑁Huei-li Lin0Department of Natural Sciences, Center for General Education, Chang Gung University, Taoyuan 333, TaiwanAssume that 𝑄 is a positive continuous function in ℝ𝑁 and satisfies some suitable conditions. We prove that the quasilinear elliptic equation −Δ𝑝𝑢+|𝑢|𝑝−2𝑢=𝑄(𝑧)|𝑢|𝑞−2𝑢 in ℝ𝑁 admits at least two solutions in ℝ𝑁 (one is a positive ground-state solution and the other is a sign-changing solution).http://dx.doi.org/10.1155/2010/673526 |
| spellingShingle | Huei-li Lin Multiple Solutions of Quasilinear Elliptic Equations in ℝ𝑁 International Journal of Differential Equations |
| title | Multiple Solutions of Quasilinear Elliptic Equations in ℝ𝑁 |
| title_full | Multiple Solutions of Quasilinear Elliptic Equations in ℝ𝑁 |
| title_fullStr | Multiple Solutions of Quasilinear Elliptic Equations in ℝ𝑁 |
| title_full_unstemmed | Multiple Solutions of Quasilinear Elliptic Equations in ℝ𝑁 |
| title_short | Multiple Solutions of Quasilinear Elliptic Equations in ℝ𝑁 |
| title_sort | multiple solutions of quasilinear elliptic equations in r𝑁 |
| url | http://dx.doi.org/10.1155/2010/673526 |
| work_keys_str_mv | AT hueililin multiplesolutionsofquasilinearellipticequationsinrn |