Normalized solutions for nonlinear fractional Kirchhoff type systems - Kong, Lingzheng; Chen, Haibo (Topological Methods in Nonlinear Analysis, 2022)
abstract% In this paper, we consider the existence of positive solutions with prescribed normalizations for strongly coupled fractional Kirchhoff type systems in the whole space R^N(N=2,3). Under constant vanishing potentials and attractive interspecies interactions, two cases are studied: one is L^2-subcritical and the other is L^2-supercritical. In the first case, we prove the existence of a positive solution by the constrained minimizing methods. In the second case, by using a minimax procedure, we prove the existence of a mountain pass type solution under high perturbations of the coupling parameter, which is also a ground state solution. Moreover, we study the L^2-critical case under certain type of trapping potentials. In this case, we are concerned with not only attractive but also repulsive interspecies interactions, and prove the existence of a positive solution by introducing some auxiliary minimization problems. These conclusions extend some known ones in previous papers.