Approximation by step functions of functions belonging to Sobolev spaces and uniqueness of solutions of?differential equations of the form $ u''=F(x,u,u')$

@inproceedings{Semenova2007ApproximationBS,
  title={Approximation by step functions of functions belonging to Sobolev spaces and uniqueness of solutions of?differential equations of the form \$ u''=F(x,u,u')\$},
  author={Tatiana Semenova},
  year={2007}
}
The paper deals with the approximation of functions belonging to the Sobolev spaces? and by functions of the form . The results obtained are applied to the study of the stability of solutions of non-linear second-order differential equations of a special form. We consider the problem of whether two solutions can coincide given supplementary information in terms of the values of the functionals , , defined on the solutions. 

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