Geodesic
Bifurcation Calculus by the Extended Functional Method
Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 1, pp. 23-38

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We justify variational principles of a new type corresponding to bifurcations of solutions for families of equations given in variational form. To illustrate the method, we consider elliptic equations with sign-indefinite nonlinearities and prove the existence of pairwise creation-annihilation bifurcations of their positive solutions. The corresponding bifurcation points are expressed via explicitly specified variational principles.
Mots-clés : bifurcation of solutions, elliptic equation
Keywords: minimax problem, sign-indefinite nonlinearity. 
@article{FAA_2007_41_1_a1,
     author = {Ya. Sh. Il'yasov},
     title = {Bifurcation {Calculus} by the {Extended} {Functional} {Method}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {23--38},
     publisher = {mathdoc},
     volume = {41},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2007_41_1_a1/}
}
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Ya. Sh. Il'yasov. Bifurcation Calculus by the Extended Functional Method. Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 1, pp. 23-38. http://geodesic.mathdoc.fr/item/FAA_2007_41_1_a1/