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Pré-publication, Document de travail

Singular solutions of some elliptic equations involving mixed absorption-reaction

Abstract : We study properties of nonnegative functions satisfying (E) −∆u + u p − M |∇u| q = 0 is a domain of R N when p > 1, M > 0 and 1 < q < p. We concentrate our analysis on the solutions of (E) with an isolated singularity, or in an exterior domain, or in the whole space. The existence of such solutions and their behaviours depend strongly on the values of the exponents p and q and in particular according to the sign of q − 2p p+1 , and when q = 2p p+1 , also on the value of the parameter M which becomes a key element. The description of the different behaviours is made possible by a sharp analysis of the radial solutions of (E).
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Pré-publication, Document de travail
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https://hal.archives-ouvertes.fr/hal-03305263
Contributeur : Laurent Veron Connectez-vous pour contacter le contributeur
Soumis le : vendredi 27 août 2021 - 15:40:10
Dernière modification le : mardi 12 octobre 2021 - 17:20:53

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  • HAL Id : hal-03305263, version 2

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Marie-Françoise Bidaut-Véron, Marta Garcia-Huidobro, Laurent Véron. Singular solutions of some elliptic equations involving mixed absorption-reaction. 2021. ⟨hal-03305263v2⟩

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