On equations of Schrödinger type with generalized potential. (Russian) Zbl 0586.34003

Rozanov, Yu. A.

Mat. Sb., N. Ser. 127(169), No. 4(8), 483-493 (1985).

The paper presents sufficient conditions for the existence and the uniqueness of solutions of equation (1) \(Lu(t)+Fu(t)=f(t),\) \(t\in S\), in a domain \(S\subseteq R^ n\) where \(L=\sum_{k}a_ kD^ k\) is a linear differential operator with generalized coefficients \(a_ k\), \(L\geq 0\) and f, F are generalized functions. F is conventionally termed the potential. Besides others it is proved that all solutions of (1) may be found as solutions of the generalized Dirichlet problem for the equation \(Lu(t)=f(t)\).

Reviewer: S.Staněk

MSC:

34A12	Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A30	Linear ordinary differential equations and systems
47E05	General theory of ordinary differential operators
34G10	Linear differential equations in abstract spaces

Keywords:

Schrödinger type equation; potential; Dirichlet problem