Domarkas, Aleksas; Ivanauskas, Feliksas; Sheibak, Miroslaw Mixed problem for a nonlinear, non-stationary system of equations of Schrödinger type. (Russian. English summary) Zbl 0648.35019 Differ. Uravn. Primen. 40, 23-33 (1987). A mixed boundary problem for a system of three nonlinear non-stationary equations is examined. The second order derivative with respect to t enters the third equation of the system. The solvability of the problem is proved in the space \(L_{\infty}(0,T;\overset\circ W^ 1_ 2(\Omega))\) for \(n=1\) for any initial conditions depending on \(\overset \circ W^ 1_ 2(\Omega)\) and for \(n=2\) for sufficiently small initial conditions in the norm \(L_ 2(\Omega)\). Cited in 1 Document MSC: 35G25 Initial value problems for nonlinear higher-order PDEs 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 35Q99 Partial differential equations of mathematical physics and other areas of application 35J10 Schrödinger operator, Schrödinger equation Keywords:Schrödinger-type equations; mixed boundary problem; solvability; initial conditions PDFBibTeX XMLCite \textit{A. Domarkas} et al., Differ. Uravn. Primen. 40, 23--33 (1987; Zbl 0648.35019)