A note on the nonlocal boundary value problem for a third order partial differential equation

Abstract

The nonlocal boundary-value problem for a third order partial differential equation {d3u(t)dt3+Adu(t)dt=f(t), 0<t<1,u(0)=γu(λ)+φ,u′(0)=αu′(λ)+Ψ,u″(0)=βu″(λ)+ξ in a Hilbert space H with a self-adjoint positive definite operator A is considered. Applying operator approach, the theorem on stability for solution of this nonlocal boundary value problem is established. In applications, the stability estimates for the solution of three nonlocal boundary value problems for the third order partial differential equations are obtained.