Multiparameter Eigenvalue Problems: methods and algorithms

Many theoretical and applied questions of mathematical physics, mechanics and other sciences form spectral problems for operator-valued functions that linearly or nonlinearly depend on two or more parameters, so-called two-parameter or multiparameter spectral problems. In this book the two approaches to the variational formulation of problems of solving both linear and nonlinear multiparameter spectral problems are proposed. There are presented and proved the algorithms for their solution. For two-parameter problems, some modifications of the algorithms for solving them in spectral formulation are offered. In particular, there are presented the application of numerical algorithms for finding the branching lines and calculating the bifurcation points of solutions of one class of nonlinear integral equations which arise in the theory of the radiation systems synthesis. The book can be useful for scientific and scientifically technological researchers who are involved in the development and application of approximate methods for solving multiparameter spectral problems. It can also be useful for postgraduate students and students of senior courses specialized in applied mathematic.