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On some nonlinear two-parameter spectral problems of mathematical physics

B. M. Podlevskyi

Institute of Applied Problems of Mechanics and Mathematics, National Academy of Sciences, Lviv, Ukraine

Abstract: 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, bifurcation points, nonlinear synthesis problem.

UDC: 519.6

Received: 29.06.2009

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