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The Bulletin of Irkutsk State University. Series Mathematics, 2013, Volume 6, Issue 4, Pages 85–106 (Mi iigum37)  

Bifurcation points of nonlinear operators: existence theorems, asymptotics and application to the Vlasov–Maxwell system

N. A. Sidorov

Irkutsk State University, 1, K . Marks St., Irkutsk, 664003

Abstract: The review of existence theorems of bifurcation points of solutions for nonlinear operator equation in Banach spaces is presented. The sufficient conditions of bifurcation of solutions of boundary-value problem for Vlasov–Maxwell system are considered. The analytical method of Lyapunov–Schmidt–Trenogin is employed.

Keywords: plasma; bifurcation points; Conley index; nonlinear analysis; Vlasov–Maxwell system; Lyapunov–Schmidt–Trenogin method.

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Citation: N. A. Sidorov, “Bifurcation points of nonlinear operators: existence theorems, asymptotics and application to the Vlasov–Maxwell system”, The Bulletin of Irkutsk State University. Series Mathematics, 6:4 (2013), 85–106

Citation in format AMSBIB
\Bibitem{Sid13}
\by N.~A.~Sidorov
\paper Bifurcation points of nonlinear operators: existence theorems, asymptotics and application to the Vlasov--Maxwell system
\jour The Bulletin of Irkutsk State University. Series Mathematics
\yr 2013
\vol 6
\issue 4
\pages 85--106
\mathnet{http://mi.mathnet.ru/iigum37}


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