Geodesic
Counting solutions in bifurcation problems
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 4, pp. 149-167

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In this paper, we use the topological degree to obtain some sharp lower bounds for the number of solutions of the parameter slices of the semi-bounded components of the set of nontrivial solutions of an abstract nonlinear equation with a trivial state. By a semi-bounded component, we mean a component that is bounded in one direction of the parameter. The spectrum of the linearization of the equation at the trivial state is not assumed to be discrete. 
@article{FPM_2006_12_4_a9,
     author = {J. Lopez-Gomez and C. Mora-Corral},
     title = {Counting solutions in bifurcation problems},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {149--167},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_4_a9/}
}
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J. Lopez-Gomez; C. Mora-Corral. Counting solutions in bifurcation problems. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 4, pp. 149-167. http://geodesic.mathdoc.fr/item/FPM_2006_12_4_a9/