A note on nonlocal boundary value problems for hyperbolic Schrödinger equations (Q437602)

Summary: The nonlocal boundary value problem \(d^2u(t)/dt^2 + Au(t) = f(t) (0 \leq t \leq 1), i(du(t)/dt) + Au(t) = g(t) (-1 \leq t \leq 0), u(0^+) = u(0^-), u_t(0^+) = u_t(0^-), Au(-1) = \alpha u(\mu) + \varphi, 0 < \mu \leq 1\), for hyperbolic Schrödinger equations in a Hilbert space \(H\) with the self-adjoint positive definite operator \(A\) is considered. The stability estimates for the solution of this problem are established. In applications, the stability estimates for solutions of the mixed-type boundary value problems for hyperbolic Schrödinger equations are obtained.