2024/04/18 by Hui Zhang, Minbo Yang, Zhang, Hui +5
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2404.12009
openalex publication_date 2024/04/18 · openalex created_date 2024/04/20 · openalex updated_date 2026/07/28
This paper is concerned with the Hamiltonian elliptic system in dimension two\aligned \ -ε2Δu+V(x)u=g(v) · amp; in ℝ2,
-ε2Δv+V(x)v=f(u) · amp; in ℝ2,.\endaligned where V∈ C(ℝ2) has local minimum points, and f,g∈ C1(ℝ) are assumed to be of exponential growth in the sense of Trudinger-Moser inequality. When V admits one or several local strict minimum points, we show the existence and concentration of single-peak and multi-peak semiclassical states respectively, as well as strong convergence and exponential decay. In addition, positivity of solutions and uniqueness of local maximum points of solutions are also studied. Our theorems extend the results of Ramos and Tavares [Calc. Var. 31 (2008) 1-25], where f and g have polynomial growth. It seems that it is the first attempt to obtain multi-peak semiclassical states for Hamiltonian elliptic system with exponential growth.