Multiplicity of semiclassical solutions for a class of nonlinear Hamiltonian elliptic system

Abstract

This article is concerned with the following Hamiltonian elliptic system: − ε 2 Δ u + ε b → ⋅ ∇ u + u + V ( x ) v = H v ( u , v ) in R N , − ε 2 Δ v − ε b → ⋅ ∇ v + v + V ( x ) u = H u ( u , v ) in R N , \left\{\begin{array}{l}-{\varepsilon }^{2}\Delta u+\varepsilon \overrightarrow{b}\cdot \nabla u+u+V\left(x)v={H}_{v}\left(u,v)\hspace{1em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{N},\\ -{\varepsilon }^{2}\Delta v-\varepsilon \overrightarrow{b}\cdot \nabla v+v+V\left(x)u={H}_{u}\left(u,v)\hspace{1em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{N},\end{array}\right. where

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一类非线性哈密顿椭圆系统半经典解的多重性

本文涉及以下哈密顿椭圆系统： - ε 2 Δ u + ε b → ⋅ ∇ u + u + V ( x ) v = R N 中的 H v ( u , v ) , - ε 2 Δ v - ε b → ⋅ ∇ v + v + V (

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