Steady state solutions of a reaction-diffusion system modeling chemotaxis
Guofang Wang and Jun-Cheng Wei
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Submission date: 16. Nov. 1998
published in: Mathematische Nachrichten, 233/234 (2002), p. 221-236
We study the following nonlinear elliptic equation
where is a smooth bounded domain in . 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 is the first (nonzero) eigenvalue of 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.