Investigation of Bifurcation Points of a Nonlinear Equations

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

“…By Corollary 1.13 it is possible, if E 1 = E 2 = H, operators B and R x (0, ε) are symmetric and condition B) is valid. Let us note that condition B) is valid in papers [16,17,15,18] about bifurcation point with potential BEq, thus r 1 = . .…”

“…Here readers may refer to his monograph [19], chapters 7-10. The bifurcation theory have been developed by various authors [5,6,16,17,15,25,18,21,22,30], etc. The approximate methods of construction branching solutions were constructed in [33,26,25,27,24,21,22,34,32,28,31,30], [36,37].…”

“…The objective of the present paper is to offer the survey of general existence theorems of bifurcation points of VM system with the given boundary conditions on potentials of an electromagnetic field both the densities of charge and current. Here we apply our results of bifurcation theory from [17,15,21,22,23] and we use the index theory [2,7,22] for the study of bifurcation points of the VM system.…”

On Application of the Lyapunov-Schmidt-Trenogin Method to Bifurcation Analysis of the Vlasov-Maxwell system

“…The objective of the present paper is to give the survey of a general existence theorems of bifurcation points of VM system with the given boundary conditions on potentials of an electromagnetic field both the densities of charge and current. Here we apply our results of bifurcation theory from [15,17,[21][22][23] and we use the index theory [2,7,22] for the study of bifurcation points of the VM system.…”

“…the theorem 1 at Υ = R 1 the generalization [17], and also other known strengthenings of M.A. Krasnoselskii theorem on a bifurcation point of odd multiplicity [6].…”