Normalized solutions for nonlinear fractional Kirchhoff type systems - Kong, Lingzheng; Chen, Haibo (Topological Methods in Nonlinear Analysis, 2022)
\begin{abstract}%In this paper, we consider the existence of positive solutions with prescribed normalizations for strongly coupled fractional Kirchhoff type systemsin the whole space $\mathbb{R}^N(N=2,3)$. 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 solutionby introducing some auxiliary minimization problems. These conclusions extend some known ones in previous papers.