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Bifurcation Results of Positive Solutions for an Indefinite Nonlinear Elliptic System II

Abstract We study local and global bifurcations of the following elliptic system where the constant a is greater than the principal eigenvalue of (-Δ,Ω), and Ω ⊂ ℝN is a bounded smooth domain (N ≤ 3). The parameters μ1,μ2 are real numbers. We identify some intervals of β in which there exist finitely many bifurcation points with respect to a trivial solution branch. In particular, when N = 1 or Ω is radial, every bifurcation branch exists globally and is characterized by a nodal property for the difference of the two components of the solutions.