Existence of solutions for a nonlocal reaction-diffusion equation in biomedical applications - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles Israel Journal of Mathematics Year : 2022

Existence of solutions for a nonlocal reaction-diffusion equation in biomedical applications

Abstract

The paper is devoted to a nonlocal semi-linear elliptic equation in R n arising in various biological and biomedical applications. The Fredholm property studied for the corresponding linear elliptic operators with discontinuous coefficients allows the application of the implicit function theorem to prove the persistence of solutions under a small perturbation of the problem. Furthermore, the existence of solutions is established by the Leray-Schauder method based on the topological degree for Fredholm and proper operators and on a priori estimates of solutions in some special weighted spaces.
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Dates and versions

hal-03840319 , version 1 (05-11-2022)

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Cite

Cristina Leon, Irina Kutsenko, Vitaly Volpert. Existence of solutions for a nonlocal reaction-diffusion equation in biomedical applications. Israel Journal of Mathematics, 2022, 248, pp.67 - 93. ⟨10.1007/s11856-022-2294-6⟩. ⟨hal-03840319⟩
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