119 citations
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math-ph2004★ 3 cited
A nonlinear singular perturbation problem
A. G. Ramm
Let F(u_\ve)+\ve(u_\ve-w)=0 \eqno{(1)} where is a nonlinear operator in a Hilbert space , is an element, and $\ve>0$ is a parameter. Assume that , and $F'(y…
math-ph2003★ 6 cited
One-dimensional inverse scattering and spectral problems
Alexander G. Ramm
Inverse scattering and spectral one-dimensional problems are discussed systematically in a self-contained way. Many novel results, due to the author are presented. The classical re…
math-ph2003★ 14 cited
On the discrepancy principle
A. G. Ramm
A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under sui…