Multiple Solutions for a Class of N-Laplacian Equations with Critical Growth and Indefinite Weight
Using the suitable Trudinger-Moser inequality and the Mountain Pass Theorem, we prove the existence of multiple solutions for a class of N-Laplacian equations with critical growth and indefinite weight -div∇uN-2∇u+VxuN-2u=λuN-2u/xβ+fx,u/xβ+ɛhx, x∈ℝN, u≠0, x∈ℝN, where 0<β<N, V(x) is an indefini...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/942092 |
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| author | Guoqing Zhang Ziyan Yao |
| author_facet | Guoqing Zhang Ziyan Yao |
| author_sort | Guoqing Zhang |
| collection | DOAJ |
| description | Using the suitable Trudinger-Moser inequality and the Mountain Pass Theorem, we prove the existence of multiple solutions for a class of N-Laplacian equations with critical growth and indefinite weight -div∇uN-2∇u+VxuN-2u=λuN-2u/xβ+fx,u/xβ+ɛhx, x∈ℝN, u≠0, x∈ℝN, where 0<β<N, V(x) is an indefinite weight, f:ℝN×ℝ→ℝ behaves like expαuN/N-1 and does not satisfy the Ambrosetti-Rabinowitz condition, and h∈(W1,N(ℝN))*. |
| format | Article |
| id | doaj-art-d72c89d636e34662932d20493e3858e3 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d72c89d636e34662932d20493e3858e32025-02-03T01:07:21ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/942092942092Multiple Solutions for a Class of N-Laplacian Equations with Critical Growth and Indefinite WeightGuoqing Zhang0Ziyan Yao1College of Sciences, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Sciences, University of Shanghai for Science and Technology, Shanghai 200093, ChinaUsing the suitable Trudinger-Moser inequality and the Mountain Pass Theorem, we prove the existence of multiple solutions for a class of N-Laplacian equations with critical growth and indefinite weight -div∇uN-2∇u+VxuN-2u=λuN-2u/xβ+fx,u/xβ+ɛhx, x∈ℝN, u≠0, x∈ℝN, where 0<β<N, V(x) is an indefinite weight, f:ℝN×ℝ→ℝ behaves like expαuN/N-1 and does not satisfy the Ambrosetti-Rabinowitz condition, and h∈(W1,N(ℝN))*.http://dx.doi.org/10.1155/2014/942092 |
| spellingShingle | Guoqing Zhang Ziyan Yao Multiple Solutions for a Class of N-Laplacian Equations with Critical Growth and Indefinite Weight Abstract and Applied Analysis |
| title | Multiple Solutions for a Class of N-Laplacian Equations with Critical Growth and Indefinite Weight |
| title_full | Multiple Solutions for a Class of N-Laplacian Equations with Critical Growth and Indefinite Weight |
| title_fullStr | Multiple Solutions for a Class of N-Laplacian Equations with Critical Growth and Indefinite Weight |
| title_full_unstemmed | Multiple Solutions for a Class of N-Laplacian Equations with Critical Growth and Indefinite Weight |
| title_short | Multiple Solutions for a Class of N-Laplacian Equations with Critical Growth and Indefinite Weight |
| title_sort | multiple solutions for a class of n laplacian equations with critical growth and indefinite weight |
| url | http://dx.doi.org/10.1155/2014/942092 |
| work_keys_str_mv | AT guoqingzhang multiplesolutionsforaclassofnlaplacianequationswithcriticalgrowthandindefiniteweight AT ziyanyao multiplesolutionsforaclassofnlaplacianequationswithcriticalgrowthandindefiniteweight |