On Eigenvalues of Nonlinear Operator Pencils with Many Parameters
The authors give the necessary and sufficient conditions of the existence of the common eigenvalues of the nonlinear several operator pencils with many parameters. The operator pencils contain also the products of these parameters in finite degree. The number of equations in these systems may be more, than the number of parameters. In the proof the authors essentially use the results of multiparameter spectral theory and the notion of the analog resultant of two and several operator pencils in many parameters.
Resultant, Operator, Multiparameter System, Eigenvalue
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