Electron. J. Diff. Equ., Vol. 2010(2010), No. 37, pp. 1-5.

An inverse boundary-value problem for semilinear elliptic equations

Ziqi Sun

We show that in dimension two or greater, a certain equivalence class of the scalar coefficient $a(x,u)$ of the semilinear elliptic equation $\Delta u\,+a(x,u)=0$ is uniquely determined by the Dirichlet to Neumann map of the equation on a bounded domain with smooth boundary. We also show that the coefficient $a(x,u)$ can be determined by the Dirichlet to Neumann map under some additional hypotheses.

Submitted January 31, 2010. Published March 14, 2010.
Math Subject Classifications: 35R30.
Key Words: Inverse Problem; Dirichlet to Neumann map.

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Ziqi Sun
Department of Mathematics and Statistics
Wichita State University, Wichita, KS 67260-0033, USA
email: ziqi.sun@wichita.edu

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