Large solutions for the Laplacian with a power nonlinearity given by a variable exponent |
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Authors: | Jorge García-Melián Julio D Rossi José C Sabina de Lis |
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Institution: | 1. Dpto. de Análisis Matemático, Universidad de La Laguna, C/Astrofísico Francisco Sánchez s/n, 38271 La Laguna, Spain;2. IMDEA Matematicas, C-IX, Campus Cantoblanco UAM, Madrid, Spain |
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Abstract: | In this paper we consider positive boundary blow-up solutions to the problem Δu=uq(x) in a smooth bounded domain Ω⊂Rn. The exponent q(x) is allowed to be a variable positive Hölder continuous function. The issues of existence, asymptotic behavior near the boundary and uniqueness of positive solutions are considered. Furthermore, since q(x) is also allowed to take values less than one, it is shown that the blow up of solutions on ∂Ω is compatible with the occurrence of dead cores, i.e., nonempty interior regions where solutions vanish. |
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Keywords: | Large solutions Existence and uniqueness Variable exponents |
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