Exact solution of one boundary-value problem

Abstract

We study the boundary-value perlodic problem u _tt −u _xx =F(x, t), u(0, t)=u(π, t)=0, u(x, t+T)=u(x, t), (x, t) is R ². By using the Vejvoda-Shtedry operator, we determine a solution of this problem.