Verified numerical computation for semilinear elliptic problems with lack of Lipschitz continuity of the first derivative
2016
In this paper, we propose a numerical method for verifying solutions to the semilinear elliptic equation -{\Delta}u=f(u) with homogeneous Dirichlet boundary condition. In particular, we consider the case in which the Fr\'echet derivative of f is not Lipschitz continuous. A numerical example for a concrete nonlinearity is presented.
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