Nondegeneracy and uniqueness for boundary blow-up elliptic problems |
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Authors: | Jorge Garcí a-Meliá n |
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Affiliation: | Dpto. de Análisis Matemático, Universidad de La Laguna, c/. Astrofísico Francisco Sánchez s/n, 38271 La Laguna, Spain |
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Abstract: | In this paper, we use for the first time linearization techniques to deal with boundary blow-up elliptic problems. After introducing a convenient functional setting, we show that the problem Δu=λa(x)up+g(x,u) in Ω, with u=+∞ on ∂Ω, has a unique positive solution for large enough λ, and determine its asymptotic behavior as λ→+∞. Here p>1, a(x) is a continuous function which can be singular near ∂Ω and g(x,u) is a perturbation term with potential growth near zero and infinity. We also consider more general problems, obtained by replacing up by eu or a “logistic type” function f(u). |
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Keywords: | Boundary blow-up problems Nondegeneracy Implicit function theorem |
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