Article Contents
Article Contents

# Multiplicity and concentration of solutions for Choquard equation via Nehari method and pseudo-index theory

• * Corresponding author: Zhongwei Tang
This work is supported by NSFC (11571040, 11671331)
• This paper concerns the following nonlinear Choquard equation:

$$$-\varepsilon^{2}\Delta w+V(x)w = \varepsilon^{-\theta}W(x)(I_\theta*(W|w|^p))|w|^{p-2}w,\quad x\in\mathbb{R}^N, ~~~~~~~~~~~~(*)$$$

where $\varepsilon>0,\ N>2,\ I_\theta$ is the Riesz potential with order $\theta\in(0,N),\ p\in\big[2,\frac{N+\theta}{N-2}\big),\ \min V>0$ and $\inf W>0$. Under proper assumptions, we explore the existence, concentration, convergence and decay estimate of semiclassical solutions for $(\ast)$. The multiplicity of solutions is established via pseudo-index theory. The existence of sign-changing solutions is achieved by minimizing the energy on Nehari nodal set.

Mathematics Subject Classification: Primary: 35J20, 35R09; Secondary: 35J61.

 Citation:

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