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

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)

Citations:

Zbl 1081.35004
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References:

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