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Weak solutions of semilinear elliptic equations with Leray-Hardy potential and measure data

Abstract : We study existence and stability of solutions of (E 1) −∆u + µ |x| 2 u + g(u) = ν in Ω, u = 0 on ∂Ω, where Ω is a bounded, smooth domain of R N , N ≥ 2, containing the origin, µ ≥ − (N −2) 2 4 is a constant, g is a nondecreasing function satisfying some integral growth assumption and ν is a Radon measure on Ω. We show that the situation differs according ν is diffuse or concentrated at the origin. When g is a power we introduce a capacity framework to find necessary and sufficient condition for solvability.
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Submitted on : Tuesday, April 2, 2019 - 6:57:12 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:35 PM
Long-term archiving on: : Wednesday, July 3, 2019 - 6:00:24 PM

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  • HAL Id : hal-02013601, version 2
  • ARXIV : 1902.04806

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Huyuan Chen, Laurent Veron. Weak solutions of semilinear elliptic equations with Leray-Hardy potential and measure data. Mathematics in Engineering, AIMS, 2019, 1 (3), pp.391-418. ⟨hal-02013601v2⟩

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