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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |