ABSTRACT
In this chapter, we describe the procedure of the perturbation method applied to self-adjoint boundary value problems for fourth-order equations. The coefficients of the equations are assumed nearly constant, and this allows us to introduce a small parameter and construct explicit analytical expressions for the sought quantities. Two schemes of the perturbation method are proposed here and are given mathematical justification: one is based on expansions in powers of the small parameter and the other is based on successive approximations. Approximations of the spectrum and the corresponding orthonormal basis are constructed with given accuracy. These can be used for approximate solution of initial boundary value problems of mathematical physics.
