A NEW METHOD FOR INVESTIGATION AND RECOGNIZING OF SELF-ADJOINT BOUNDARY VALUE PROBLEMS

Boundary value problems (BVPs) are one of the most important fields in engineering and mathematical physics. In self-adjoint case of these problems, there are some facilities to solve them, such as eigenvalues of adjoint equations are real numbers and associated eigenfunctions make an orthogonal basis system. In this paper a new method for investigation of self-adjoint B.V.Ps including ordinary differential equations (O.D.Es) is introduced. Based on this method, at first, some necessary conditions are obtained by making use of fundamental solutions of adjoint equations. Then an algebraic system is made by this necessary conditions and boundary conditions of given boundary value problem. Finally, by making use of Lagrangian identity and boundary values of unknown function, sufficient conditions for having a self-adjoint problem are presented.