Positive solutions of higher order quasilinear elliptic equations
The higher order quasilinear elliptic equation −Δ(Δp(Δu))=f(x,u) subject to Dirichlet boundary conditions may have unique and regular positive solution. If the domain is a ball, we obtain a priori estimate to the radial solutions via blowup. Extensions to systems and general domains are also present...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337502204030 |
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| _version_ | 1832551346831622144 |
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| author | Marcelo Montenegro |
| author_facet | Marcelo Montenegro |
| author_sort | Marcelo Montenegro |
| collection | DOAJ |
| description | The higher order quasilinear elliptic equation −Δ(Δp(Δu))=f(x,u) subject to Dirichlet boundary
conditions may have unique and regular positive solution. If the
domain is a ball, we obtain a priori estimate to the radial
solutions via blowup. Extensions to systems and general domains
are also presented. The basic ingredients are the maximum
principle, Moser iterative scheme, an eigenvalue problem, a
priori estimates by rescalings, sub/supersolutions, and
Krasnosel'skiĭ fixed point theorem. |
| format | Article |
| id | doaj-art-19374b5d13824bf3b0eb3e38f64cb27e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-19374b5d13824bf3b0eb3e38f64cb27e2025-02-03T06:01:41ZengWileyAbstract and Applied Analysis1085-33751687-04092002-01-017842345210.1155/S1085337502204030Positive solutions of higher order quasilinear elliptic equationsMarcelo Montenegro0Universidade Estadual de Campinas, IMECC, Departamento de Matemática, Caixa Postal 6065, CEP 130813-970, Campinas, SP, BrazilThe higher order quasilinear elliptic equation −Δ(Δp(Δu))=f(x,u) subject to Dirichlet boundary conditions may have unique and regular positive solution. If the domain is a ball, we obtain a priori estimate to the radial solutions via blowup. Extensions to systems and general domains are also presented. The basic ingredients are the maximum principle, Moser iterative scheme, an eigenvalue problem, a priori estimates by rescalings, sub/supersolutions, and Krasnosel'skiĭ fixed point theorem.http://dx.doi.org/10.1155/S1085337502204030 |
| spellingShingle | Marcelo Montenegro Positive solutions of higher order quasilinear elliptic equations Abstract and Applied Analysis |
| title | Positive solutions of higher order quasilinear elliptic equations |
| title_full | Positive solutions of higher order quasilinear elliptic equations |
| title_fullStr | Positive solutions of higher order quasilinear elliptic equations |
| title_full_unstemmed | Positive solutions of higher order quasilinear elliptic equations |
| title_short | Positive solutions of higher order quasilinear elliptic equations |
| title_sort | positive solutions of higher order quasilinear elliptic equations |
| url | http://dx.doi.org/10.1155/S1085337502204030 |
| work_keys_str_mv | AT marcelomontenegro positivesolutionsofhigherorderquasilinearellipticequations |