A note on the implicit function theorem for quasi-linear eigenvalue problems |
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Authors: | Robin Nittka |
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Institution: | Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany |
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Abstract: | We consider the quasi-linear eigenvalue problem −Δpu=λg(u) subject to Dirichlet boundary conditions on a bounded open set Ω, where g is a locally Lipschitz continuous function. Imposing no further conditions on Ω or g, we show that for λ near zero the problem has a bounded solution which is unique in the class of all small solutions. Moreover, this curve of solutions parameterized by λ depends continuously on the parameter. |
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Keywords: | primary 35P30 secondary 47J07 |
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