The existence of multiple solutions for perturbed equations is shown near a manifold of solutions of an unperturbed equation via the Nielsen fixed point theory.
@article{118621, author = {Michal Fe\v ckan}, title = {Multiple perturbed solutions near nondegenerate manifolds of solutions}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {34}, year = {1993}, pages = {635-643}, zbl = {0795.58006}, mrnumber = {1263793}, language = {en}, url = {http://dml.mathdoc.fr/item/118621} }
Fečkan, Michal. Multiple perturbed solutions near nondegenerate manifolds of solutions. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 635-643. http://gdmltest.u-ga.fr/item/118621/
Nielsen fixed point theory and nonlinear equations, to appear in Journal Differential Equations.
Critical Point Theory and Hamiltonian Systems, in Appl. Math. Sci., Vol. 74 (1989). (1989) | MR 0982267 | Zbl 0676.58017
Topological identification of multiple solutions to parametrized nonlinear equations, Pacific J. Math. 131 (1988), 51-69. (1988) | MR 0917865 | Zbl 0615.47042
Stable Mappings and their Singularities, Springer-Verlag New York (1973). (1973) | MR 0341518 | Zbl 0294.58004
Lectures on Nielsen Fixed Point Theory, in Contemporary Math., Vol 14 (1983). (1983) | MR 0685755 | Zbl 0512.55003
The G-invariant implicit function theorem in infinite dimensions II, Proc. Royal Soc. Edinburgh 102 A, (1986), 211-220. (1986) | MR 0852355 | Zbl 0601.58013
Multiple closed orbits for perturbed Keplerian problems, Journal Differential Equations 96 (1992), 283-94. (1992) | MR 1156662 | Zbl 0759.34033
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag New York (1983). (1983) | MR 0709768 | Zbl 0515.34001
Problems with nonlinear boundary value conditions, Comment. Math. Univ. Carolinae 33 (1992), 597-604. (1992) | MR 1240180
Differential Topology, Springer-Verlag New York (1976). (1976) | MR 0448362 | Zbl 0356.57001