Numerical Algorithms of Finding the Branching Lines and Bifurcation Points of Solutions for One Class of Nonlinear Integral Equations [chapter]

B. M.
2012 Nonlinearity, Bifurcation and Chaos - Theory and Applications  
Application of the cited above approach to the nonlinear integral operator arising at synthesis of the antenna systems according to the given amplitude directivity pattern, brings to the nonlinear two-parameter eigenvalue problem T   analytically depending on two spectral parameters  and  . The essential difference of the two-parameter problems from the one-parameter ones is that the two-parameter problem can not have at all the solutions or, on the contrary, to have them as a continuum
more » ... which in the case of real parameters are the curves of eigenvalues. Such problems are still not investigated because there are still many open questions connected with this problem such as, for example, the existence of solutions and their number, and also the development of numerical methods of solving such spectral problems for algebraic, differential and integral equations.     2 sin sin    
doi:10.5772/48735 fatcat:bssq3exlazaznpdwcpwutgvp2m