## Functionals on solutions of the Cauchy problem for the Schrödinger equation with degeneration on a half-line.(Russian, English)Zbl 1136.35443

Zh. Vychisl. Mat. Mat. Fiz. 44, No. 9, 1654-1673 (2004); translation in Comput. Math. Math. Phys. 44, No. 9, 1573-1591 (2004).
The Cauchy problem for the Schrödinger equation with the operator degenerating on semi-axis and the class of regularized Cauchy problems with evenly elliptic operators which solution approximates the singular problems solutions is considered. Strong and weak convergence of family of solutions of regularized problems is investigated. The convergence of values of any class of quadratic functionals on regularized problems solutions at the tendency to $$0$$ regularization parameter is investigated also.

### MSC:

 35Q40 PDEs in connection with quantum mechanics 35J10 Schrödinger operator, Schrödinger equation 47N20 Applications of operator theory to differential and integral equations
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