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Journal Articles Discrete and Continuous Dynamical Systems - Series A Year : 2022

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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Origin : Files produced by the author(s)
Origin : Files produced by the author(s)

Dates and versions

hal-03305263 , version 1 (28-07-2021)
hal-03305263 , version 2 (27-08-2021)

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Marie-Françoise Bidaut-Véron, Marta Garcia-Huidobro, Laurent Véron. Singular solutions of some elliptic equations involving mixed absorption-reaction. Discrete and Continuous Dynamical Systems - Series A, 2022, 42, pp.3861-3930. ⟨10.3934/dcds.2022036⟩. ⟨hal-03305263v2⟩
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