Steady State Solutions of a Reaction‐Diffusion System Modeling Chemotaxis

We study the following nonlinear elliptic equation where Ω is a smooth bounded domain in ℝ2. This equation arises in the study of stationary solutions of a chemotaxis system proposed by Keller and Segel. Under the condition that for m =1,2,…, where λ1 is the first (nonzero) eigenvalue of —Δ under the Neumann boundary condition, we establish the existence of a solution to the above equation. Our idea is a combination of Struwe's technique and blow up analysis for a problem with Neumann boundary condition.

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