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Global uniqueness for a two-dimensional semilinear elliptic inverse problem. (English) Zbl 0849.35148
Authors’ abstract: For a general class of nonlinear Schrödinger equation \(- \Delta u+ a(x, u)= 0\) in a bounded planar domain \(\Omega\) we show that the function \(a(x, u)\) can be recovered from knowledge of the corresponding Dirichlet-to-Neumann map on the boundary \(\partial \Omega\).

MSC:
35R30 Inverse problems for PDEs
35J10 Schrödinger operator, Schrödinger equation
35J25 Boundary value problems for second-order elliptic equations
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