Abstract
The paper is concerned with the study of small stable cycles of autonomous quasilinear systems depending on a parameter. Sufficient conditions are presented for the existence of such cycles for control theory equations with scalar nonlinearities. The principal distinction of the case considered from usual results on Hopf bifurcations is that the linear part of the problem is degenerate for all ...
Abstract
The paper is concerned with the study of small stable cycles of autonomous quasilinear systems depending on a parameter. Sufficient conditions are presented for the existence of such cycles for control theory equations with scalar nonlinearities. The principal distinction of the case considered from usual results on Hopf bifurcations is that the linear part of the problem is degenerate for all the parameter values (not only at a bifurcation point). Small sublinear nonlinearities play the main role in our results. The proofs are based on the theory of monotone operators.
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