Multiple solutions for a problem with resonance involving the p-Laplacian
In this paper we will investigate the existence of multiple solutions for the problem (P) −Δpu+g(x,u)=λ1h(x)|u|p−2u, in Ω, u∈H01,p(Ω) where Δpu=div(|∇u|p−2∇u) is the p-Laplacian operator, Ω⫅ℝN is a bounded domain with smooth boundary...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
1998-01-01
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| Series: | Abstract and Applied Analysis |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S1085337598000517 |
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| _version_ | 1832552064129957888 |
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| author | C. O. Alves P. C. Carrião O. H. Miyagaki |
| author_facet | C. O. Alves P. C. Carrião O. H. Miyagaki |
| author_sort | C. O. Alves |
| collection | DOAJ |
| description | In this paper we will investigate the existence of multiple
solutions for the problem (P) −Δpu+g(x,u)=λ1h(x)|u|p−2u, in Ω, u∈H01,p(Ω) where Δpu=div(|∇u|p−2∇u) is the p-Laplacian operator, Ω⫅ℝN is a bounded domain with smooth boundary, h and g are bounded functions, N≥1 and 1<p<∞. Using the Mountain Pass Theorem and the Ekeland Variational Principle, we will show the existence of at least three solutions for (P). |
| format | Article |
| id | doaj-art-19c1192f7367438a9ebe0e25e95762e1 |
| institution | Kabale University |
| issn | 1085-3375 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-19c1192f7367438a9ebe0e25e95762e12025-02-03T05:59:35ZengWileyAbstract and Applied Analysis1085-33751998-01-0131-219120110.1155/S1085337598000517Multiple solutions for a problem with resonance involving the p-LaplacianC. O. Alves0P. C. Carrião1O. H. Miyagaki2Departamento de matemática e Estatística, Universidade Federal da Paraíba, Campina Grande 58109-970, (PB), BrazilDepartamento de Matemática, Universidade Federal de Minas Gerais, Belo Horizonte 31270-010, (MG), BrazilDepartamento de Matemática, Universidade Federal de Viçosa, Viçosa 36571-000, (MG), BrazilIn this paper we will investigate the existence of multiple solutions for the problem (P) −Δpu+g(x,u)=λ1h(x)|u|p−2u, in Ω, u∈H01,p(Ω) where Δpu=div(|∇u|p−2∇u) is the p-Laplacian operator, Ω⫅ℝN is a bounded domain with smooth boundary, h and g are bounded functions, N≥1 and 1<p<∞. Using the Mountain Pass Theorem and the Ekeland Variational Principle, we will show the existence of at least three solutions for (P).http://dx.doi.org/10.1155/S1085337598000517Radial solutionsCritical Sobolev exponentsPalais-Smale conditionMountain Pass Theorem. |
| spellingShingle | C. O. Alves P. C. Carrião O. H. Miyagaki Multiple solutions for a problem with resonance involving the p-Laplacian Abstract and Applied Analysis Radial solutions Critical Sobolev exponents Palais-Smale condition Mountain Pass Theorem. |
| title | Multiple solutions for a problem with resonance involving the
p-Laplacian |
| title_full | Multiple solutions for a problem with resonance involving the
p-Laplacian |
| title_fullStr | Multiple solutions for a problem with resonance involving the
p-Laplacian |
| title_full_unstemmed | Multiple solutions for a problem with resonance involving the
p-Laplacian |
| title_short | Multiple solutions for a problem with resonance involving the
p-Laplacian |
| title_sort | multiple solutions for a problem with resonance involving the p laplacian |
| topic | Radial solutions Critical Sobolev exponents Palais-Smale condition Mountain Pass Theorem. |
| url | http://dx.doi.org/10.1155/S1085337598000517 |
| work_keys_str_mv | AT coalves multiplesolutionsforaproblemwithresonanceinvolvingtheplaplacian AT pccarriao multiplesolutionsforaproblemwithresonanceinvolvingtheplaplacian AT ohmiyagaki multiplesolutionsforaproblemwithresonanceinvolvingtheplaplacian |