Multi-bump solutions for the nonlinear magnetic Schrödinger equation with logarithmic nonlinearity

2024/01/14 by Jun Wang, Zhaoyang Yin, Wang, Jun +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2401.07199

openalex publication_date 2024/01/14 · openalex created_date 2024/01/18 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the following nonlinear magnetic Schrödinger equation with logarithmic nonlinearity -(∇+iA(x))²u+λV(x)u =|u|^q-2u+ulog |u|², u∈ H¹(ℝ^N,ℂ), where the magnetic potential A ∈ L_{l o c}²(ℝ^N, ℝ^N), 20 is a parameter and the nonnegative continuous function V: ℝ^N → ℝ has the deepening potential well. Using the variational methods, we obtain that the equation has at least 2^k-1 multi-bump solutions when λ>0 is large enough.

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