Boundedness in a parabolic-elliptic chemotaxis system with logistic source involving the exponents depending on the spatial variables and nonlinear signal productions

This paper considers the global boundedness of solutions to the parabolic-elliptic chemotaxis system with a logistic source involving exponents that depend on spatial variables and nonlinear signal production: (Formula presented.) where (Formula presented.), μ, (Formula presented.), and (Formula presented.) is a measurable function, subject to the homogeneous Neumann boundary conditions in a bounded domain (Formula presented.) with smooth boundary. We prove that if either (Formula presented.), (Formula presented.) or (Formula presented.) with (Formula presented.) or (Formula presented.) with (Formula presented.), (Formula presented.) or (Formula presented.), then the above system possesses a unique global bounded classical solution.