ABSTRACT
Some important classes of dynamical systems occurring in physics and mechanics are described by higher-order (4th, 6th, 8th, etc.) equations. For many problems, separation of the time and the spatial variables results in eigenvalue problems of Sturm-Liouville type. Theoretical and numerical methods of solving such problems for higher-order equations whose coefficients have considerable variation have not been developed to a desirable extent or are altogether absent. In Chapters 6, 7, and 8, we suggest constructive approaches to the solution of self-conjugate fourth-order eigenvalue problems with different types of boundary conditions. Our numerical-analytical methods possess great generality and can be extended to arbitrary self-conjugate problems with a scalar argument, and also to some systems of partial differential equations.
