Geodesic
On some nonlinear two-parameter spectral problems of mathematical physics
Matematičeskoe modelirovanie, Tome 22 (2010) no. 5, pp. 131-145

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In frameworks of simple mathematical model the nonlinear synthesis problems of a plane equidistant antenna array according to the given requirements to an amplitude directivity pattern is considered. At finding the branching lines of solutions of nonlinear integral equations obtained as a result of solution of the synthesis problem, the two-parameter eigenvalue problems with spectral parameters analytically including in a kernel of the linearized integral operator are arisen. For such problems the numerical algorithms of finding the eigenvalue curves and the bifurcation points are considered. The numerical examples are presented.
Keywords: nonlinear two-parameter spectral problem, branching lines, nonlinear synthesis problem.
Mots-clés : bifurcation points 
@article{MM_2010_22_5_a12,
     author = {B. M. Podlevskyi},
     title = {On some nonlinear two-parameter spectral problems of mathematical physics},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {131--145},
     publisher = {mathdoc},
     volume = {22},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2010_22_5_a12/}
}
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B. M. Podlevskyi. On some nonlinear two-parameter spectral problems of mathematical physics. Matematičeskoe modelirovanie, Tome 22 (2010) no. 5, pp. 131-145. http://geodesic.mathdoc.fr/item/MM_2010_22_5_a12/