Time-nonlocal problems for Schrödinger type equations. II: Results for specific problems. (English. Russian original) Zbl 1082.35055

Gordeziani, D. G.; Avalishvili, G. A.

Differ. Equ. 41, No. 6, 852-859 (2005); translation from Differ. Uravn. 41, No. 6, 813-819 (2005).

Summary: We analyze time-nonlocal problems for Schrödinger type equations and systems with particular nonclassical initial conditions which are an analog of nonlocal boundary conditions considered. Problems of that type generalize periodic problems with respect to the time variable and can be treated as control problems with initial conditions. We show that, for a specific form of time-nonlocal problems, the existence and uniqueness of their solutions depend on the arithmetic properties of expressions containing time moments and geometric characteristics of the space domain.
Part I, cf. Differ. Equ. 41, No. 5, 703–711 (2005); translation from Differ. Uravn. 41, No. 5, 670–677 (2005; Zbl 1081.35004).

MSC:

35G10	Initial value problems for linear higher-order PDEs
47D08	Schrödinger and Feynman-Kac semigroups
34G10	Linear differential equations in abstract spaces
35A05	General existence and uniqueness theorems (PDE) (MSC2000)

Keywords:

nonclassical initial conditions; control problems with initial conditions

Citations:

Zbl 1081.35004

References:

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