In this work, we are concerned with a class of parabolic-elliptic chemotaxis systems with the prototype given by
$\left\{ \begin{array}{lll}&u_t = \nabla\cdot(\nabla u-\chi u\nabla v)+au-bu^\theta, &x\in \Omega, t>0, \\&0 = \Delta v -v+u^\kappa, & x\in \Omega, t>0 \end{array}\right.$
with nonnegative initial condition for $u$ and homogeneous Neumann boundary conditions in a smooth bounded domain $Ω\subset \mathbb{R}^n(n≥ 2)$, where $χ, b, κ>0$, $a∈ \mathbb{R}$ and $θ>1$.
First, using different ideas from [
$κ+1<\max\{θ, 1+\frac{2}{n}\}$
or
$θ = κ+1, \ \ b≥ \frac{(κ n-2)}{κ n}χ.$
Next, carrying out bifurcation from "old multiplicity", we show that the corresponding stationary system exhibits pattern formation for an unbounded range of chemosensitivity $χ$ and the emerging patterns converge weakly in $ L^θ(Ω)$ to some constants as $χ \to ∞$. This provides more details and also fills up a gap left in Kuto et al. [
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