Let , k = const > 0, j = 1,2, . Suppose that (*) for all k > 0, where p is an arbitrary fixed bounded piecewise-analytic function on [0,1], which changes sign finitely many times, and solves the problem , 0 ≤ x ≤ 1, , . It is proved that (*) implies p = 0. This result is applied to an inverse problem for a heat equation.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-3-6, author = {A. G. Ramm}, title = {Property C for ODE and Applications to an Inverse Problem for a Heat Equation}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, volume = {57}, year = {2009}, pages = {243-249}, zbl = {1197.34174}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-3-6} }
A. G. Ramm. Property C for ODE and Applications to an Inverse Problem for a Heat Equation. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) pp. 243-249. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-3-6/