Ayazoglu, Rabil2026-02-282026-02-2820240044-22751420-9039https://doi.org/10.1007/s00033-024-02394-6https://hdl.handle.net/20.500.12403/5917We study the quasilinear attraction-repulsion chemotaxis system of parabolic-elliptic type with logistic source involving the exponents depending on the spatial variables: u(t )= Delta u-chi del & sdot; (u (u+1)(r-1)del upsilon) + xi del & sdot; (u (u+1)(r-1)del omega) + au-bu(m(x)), 0 = Delta upsilon-beta upsilon + alpha u, 0 = Delta omega - delta omega + gamma u, where alpha, beta, delta, gamma, chi, xi, b > 0, a >= 0, r is an element of R and m: Omega -> (1, infinity) is a measurable function, subject to the homogeneous Neumann boundary conditions in a bounded domain R-N (N >= 1) with smooth boundary. We prove that this system possesses a unique global bounded classical solution, which is an extension of known results, if the repulsion cancels the attraction in the sense that (balance) chi alpha = xi gamma with ess inf(x is an element of Omega)m(x)>{r+(N-2)(+)/N, 1}, and if the attraction prevails over the repulsion in the sense that chi alpha > xi gamma with ess inf(x is an element of Omega)m(x) > max {r+1, 1}, and if the repulsion prevails over the attraction in the sense that chi alpha < xi gamma.eninfo:eu-repo/semantics/closedAccessAttraction-repulsionChemotaxis systemLogistic source involving the exponents depending on the spatial variablesGlobal boundednessArticle76110.1007/s00033-024-02394-62-s2.0-85213061939Q1WOS:001386049100001Q2