N-Laplacian equations in ℝN with critical growth
We study the existence of nontrivial solutions to the following problem: {u∈W1,N(ℝN),u≥0 and−div(|∇u|N−2∇u)+a(x)|u|N−2u=f(x,u) in ℝN(N≥2), where a is a continuous function which is coercive, i.e., a(x)→∞ as |x|→∞ and the nonlinearity f behaves like exp(α|u|N/(N−1)) when |u|→∞....
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1997-01-01
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| Series: | Abstract and Applied Analysis |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S1085337597000419 |
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| _version_ | 1832551939732144128 |
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| author | João Marcos B. do Ó |
| author_facet | João Marcos B. do Ó |
| author_sort | João Marcos B. do Ó |
| collection | DOAJ |
| description | We study the existence of nontrivial solutions to the following problem: {u∈W1,N(ℝN),u≥0 and−div(|∇u|N−2∇u)+a(x)|u|N−2u=f(x,u) in ℝN(N≥2), where a is a continuous function which is coercive, i.e., a(x)→∞ as |x|→∞
and the nonlinearity f behaves like exp(α|u|N/(N−1)) when |u|→∞. |
| format | Article |
| id | doaj-art-351f2a45fe2b427397f297dac20d09f9 |
| institution | Kabale University |
| issn | 1085-3375 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-351f2a45fe2b427397f297dac20d09f92025-02-03T05:59:55ZengWileyAbstract and Applied Analysis1085-33751997-01-0123-430131510.1155/S1085337597000419N-Laplacian equations in ℝN with critical growthJoão Marcos B. do Ó0Departamento de Matemática, Universidade Federal da Paraíba, João Pessoa 58059.900, Pb, BrazilWe study the existence of nontrivial solutions to the following problem: {u∈W1,N(ℝN),u≥0 and−div(|∇u|N−2∇u)+a(x)|u|N−2u=f(x,u) in ℝN(N≥2), where a is a continuous function which is coercive, i.e., a(x)→∞ as |x|→∞ and the nonlinearity f behaves like exp(α|u|N/(N−1)) when |u|→∞.http://dx.doi.org/10.1155/S1085337597000419Elliptic equationsp-Laplaciancritical growthMountain Pass theoremTrudinger-Moser inequality. |
| spellingShingle | João Marcos B. do Ó N-Laplacian equations in ℝN with critical growth Abstract and Applied Analysis Elliptic equations p-Laplacian critical growth Mountain Pass theorem Trudinger-Moser inequality. |
| title | N-Laplacian equations in ℝN with critical growth |
| title_full | N-Laplacian equations in ℝN with critical growth |
| title_fullStr | N-Laplacian equations in ℝN with critical growth |
| title_full_unstemmed | N-Laplacian equations in ℝN with critical growth |
| title_short | N-Laplacian equations in ℝN with critical growth |
| title_sort | n laplacian equations in rn with critical growth |
| topic | Elliptic equations p-Laplacian critical growth Mountain Pass theorem Trudinger-Moser inequality. |
| url | http://dx.doi.org/10.1155/S1085337597000419 |
| work_keys_str_mv | AT joaomarcosbdoo nlaplacianequationsinrnwithcriticalgrowth |