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

The paper is devoted to a nonlocal semi-linear elliptic equation in ℝn 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. © 2022, The Hebrew University of Jerusalem.