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Deformations of functionals and bifurcations of extremals. (English. Russian original) Zbl 1136.47041
Math. Notes 81, No. 1, 61-71 (2007); translation from Mat. Zametki 81, No. 1, 70-82 (2006).
The present paper is devoted to the bifurcation-point problem for multivalued operators of monotonic type. The paper contains an analysis of two illustrative examples, which are of interest on their own.
The authors summary is: “We study homology characteristics of critical values and extremals of Lipschitz functionals defined on bounded closed convex subsets of a reflexive space that are invariant under deformations. Sufficient conditions for the existence of a bifurcation point of a multivalued potential operator (the switch principle for the typical number of an extremal) are established.”

47J15 Abstract bifurcation theory involving nonlinear operators
47H11 Degree theory for nonlinear operators
49J40 Variational inequalities
47H50 Potential operators (MSC2000)
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