The concentration behavior of ground state solutions for nonlinear Dirac equation. (June 2020) - Ding, Yanheng; Yu, Yuanyang
Abstract: In this paper, we study the following nonlinear Dirac equation − i ε ∑ k = 1 3 α k ∂ k u + a β u + V ( x ) u = K ( x ) f ( | u | ) u, in R 3, where ε > 0 is a small parameter, a > 0 is a constant, α 1, α 2, α 3 and β are 4 × 4 Pauli–Dirac matrices, V, K and f are continuous but are not necessarily of class C 1 . We prove the existence of ground state solution by using variational methods, and we determine a concrete set related to the potentials V and K as the concentration position of these ground state solutions as ε → 0 . Moreover, we consider some properties of these ground state solutions, such as convergence and exponential decay estimate. The result presented in this paper generalizes the result in Ding and Liu (2012).