Geodesic
Non-local investigation of bifurcations of solutions of non-linear elliptic equations
Izvestiya. Mathematics , Tome 66 (2002) no. 6, pp. 1103-1130

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We justify the projective fibration procedure for functionals defined on Banach spaces. Using this procedure and a dynamical approach to the study with respect to parameters, we prove that there are branches of positive solutions of non-linear elliptic equations with indefinite non-linearities. We investigate the asymptotic behaviour of these branches at bifurcation points. In the general case of equations with $p$-Laplacian we prove that there are upper bounds of branches of positive solutions with respect to the parameter. 
@article{IM2_2002_66_6_a1,
     author = {Ya. Sh. Il'yasov},
     title = {Non-local investigation of bifurcations of solutions of non-linear elliptic equations},
     journal = {Izvestiya. Mathematics },
     pages = {1103--1130},
     publisher = {mathdoc},
     volume = {66},
     number = {6},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2002_66_6_a1/}
}
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Ya. Sh. Il'yasov. Non-local investigation of bifurcations of solutions of non-linear elliptic equations. Izvestiya. Mathematics , Tome 66 (2002) no. 6, pp. 1103-1130. http://geodesic.mathdoc.fr/item/IM2_2002_66_6_a1/