The existence of infinitely many bifurcating branches
Hans-Jörg Ruppen · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1985
Synopsis We consider the non-linear problem −Δ u ( x )− f ( x , u ( x )) = λ u ( x ) for x ∈ℝ N and u ∈ W 1,2 (ℝ N ). We show that, under suitable conditions on f , there exist infinitely many branches all bifurcating from the lowest point of the continuous spectrum λ = 0. The method used in the proof is based on a theorem of Ljusternik-Schnirelman type for the free case.