A Note on Nonlocal Boundary Value Problems for Hyperbolic Schrödinger Equations

Abstract

The nonlocal boundary value problem $d^{2}u\left(t\right)/d{t}^2+Au\left(t\right)=f\left(t\right)\left(0\le t\le 1\right)$, $i\left(du\left(t\right)/dt\right)+Au\left(t\right)=g\left(t\right)\left(-1\le t\le 0\right)$, $u\left(0^{+}\right)=u\left(0^{-}\right)$, $u_t\left(0^{+}\right)=u_t\left(0^{-}\right)$, $Au(-1)=\alpha u\left(\mu \right)+\phi$, , 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.