A Note on Nonlocal Boundary Value Problems for Hyperbolic Schrödinger Equations

Abstract EN

The nonlocal boundary value problem d2u(t)/dt2+Au(t)=f(t) (0≤t≤1), i(du(t)/dt)+Au(t)=g(t) (-1≤t≤0), u(0+)=u(0-), ut(0+)=ut(0-), Au(-1)=αu(μ)+φ, 0<μ≤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.