Global Weak Solution in a p-Laplacian Attraction-Repulsion Chemotaxis System with Nonlinear Sensitivity and Signal Production

We consider the following p-Laplacian chemotaxis system with logistic source and nonlinear production: \ array{ll uₓ= (| u|^p-2 u) - (u^ v) + (u^ w) +f (u), \;\;x, \;t0, \\ vₓ= v- v+ u^k₁, \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x, \;t0, \\ 0= w- w+ u^k₂, \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x, \;t0, array. where, , , , , , , , k₁, k₂ 0, p 2, R^n (n2) is a smoothly bounded domain. The logistic-type source f (s) - s^m for R, 0 and m1. We obtain the global boundedness of solutions if (i) m\2k₁, p{p-1-1\}, or (ii) k₂\2k₁-, p{p-1--1\} with m\2, 2, 2\.