On the Separation of Variables for Boundary Value Problems with Nonlocal Boundary Relations
Mokin A.Ju.
"Математика. Компьютер. Образование". Cб. трудов XV международной конференции. Под общей редакцией Г.Ю. Ризниченко Ижевск: Научно-издательский центр "Регулярная и хаотическая динамика", 2008. Vol. 2, 276pp. Pp. 46-54. (accepted)
A boundary value problem for partial differential equation with nonlocal boundary relations of special type is resolved by means of slight modification of the separation of variables method. Ordinal differential operator of the second order subject to boundary conditions of the main problem is not self-adjoint. The system of eigenfunctions, which the operator generates, has not basis property in L2[0,1] space. A special system of functions is proposed to expand the solution of the boundary value problem.
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