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antipodal Benci and Cerami bounded smooth domain cat(ft change sign exactly Classificação connected components Constraint Qualification continuous function Craveiro e J. P. O. critical points denote dist(x Domain Topology ELLIPTIC EQUATION EQUATION WITH SYMMETRY equivariant category equivariant homotopy equivalences Equivariant Ljusternik-Schnirelmann equivariant map equivariantly homotopic Filidor fixed there exists ft C RN Furtado G ft G Nx Guillén González inclusion map inf Ex(u involution J. P. O. Santos J.M. Martínez Lemma Ljusternik-Schnirelmann category M. A. Rojas Medar M.L. Schuverdt Marcelo F Mari Sano Marko Martínez and M.L. Métodos Minimal Nodal Solutions Nehari manifold NUMBER OF NODAL number of solutions Números de Fibonacci Palais-Smale condition positive solutions problem PI Proof Q+ are equivariant r-invariant RELATÓRIOS DE PESQUISA Ricardo Rojas-Medar Ronaldo Dias Sandra Augusta Santos semilinear problem Sequence sign exactly once solutions which change subset Takeyama Theorem 1.1 topological space topology of ft u(tx Uj(x