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Boundary singular solutions of a class of equations with mixed absorption-reaction

Abstract : We study properties of positive functions satisfying (E) −∆u + u p − M |∇u| q = 0 is a domain Ω or in R N + when p > 1 and 1 < q < min{p, 2}. We concentrate our research on the solutions of (E) vanishing on the boundary except at one point. This analysis depends on the existence of separable solutions in R N +. We consruct various types of positive solutions with an isolated singularity on the boundary. We also study conditions for the removability of compact boundary sets and the Dirichlet problem associated to (E) with a measure for boundary data.
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https://hal.archives-ouvertes.fr/hal-02909840
Contributor : Laurent Veron Connect in order to contact the contributor
Submitted on : Tuesday, January 11, 2022 - 4:38:19 PM
Last modification on : Thursday, January 13, 2022 - 4:58:17 AM

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  • HAL Id : hal-02909840, version 3
  • ARXIV : 2007.16097

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Marie-Françoise Bidaut-Veron, Marta Garcia-Huidobro, Laurent Veron. Boundary singular solutions of a class of equations with mixed absorption-reaction. Calculus of Variations and Partial Differential, In press. ⟨hal-02909840v3⟩

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