Abstract
In this paper, we consider the equation
where \(\varepsilon \) is a small parameter, V is the external potential, \(A_i(i=0,1,2)\) is the gauge field and \(f\in C({\mathbb {R}}, {\mathbb {R}})\) is 5-superlinear growth. By using variational methods and analytic technique, we prove that this system possesses a ground state solution \(u_\varepsilon \). Moreover, our results show that, as \(\varepsilon \rightarrow 0\), the global maximum point \(x_\varepsilon \) of \(u_\varepsilon \) must concentrate at the global minimum point \(x_0\) of V.
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Wang, LJ., Li, GD. & Tang, CL. Existence and Concentration of Semi-classical Ground State Solutions for Chern–Simons–Schrödinger System. Qual. Theory Dyn. Syst. 20, 40 (2021). https://doi.org/10.1007/s12346-021-00480-y
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DOI: https://doi.org/10.1007/s12346-021-00480-y