Local behaviour of the solutions of the Chipot-Weissler equation - Archive ouverte HAL Access content directly
Journal Articles Calculus of Variations and Partial Differential Equations Year : 2023

Local behaviour of the solutions of the Chipot-Weissler equation

Laurent Véron

Abstract

We study the local properties of positive solutions of the equation −∆u = u p − m |∇u| q in a punctured domain Ω \ {0} of R N or in a exterior domain R N \ B r0 in the range min{p, q} > 1 and m > 0. We prove a series of a priori estimates depending p and q, and of the sign of q − 2p p+1 and q − p. Using various techniques we obtain removability results for singular sets and we give a precise description of behaviour of solutions near an isolated singularity or at infinity in R N .
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Dates and versions

hal-04027231 , version 1 (13-03-2023)
hal-04027231 , version 2 (09-09-2023)

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Marie-Françoise Bidaut-Véron, Laurent Véron. Local behaviour of the solutions of the Chipot-Weissler equation. Calculus of Variations and Partial Differential Equations, In press, ⟨10.1007/s00526-023-02580-w⟩. ⟨hal-04027231v2⟩
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