Multiple normalized solutions for a class of dipolar Gross-Pitaveskii equation with a mass subcritical perturbation

Abstract

In this paper, we study the existence of multiple normalized solutions to the following dipolar Gross-Pitaveskii equation with a mass subcritical perturbation \begin{align*} \left\{ \begin{array}{lll} -\frac{1}{2}\Delta u+\mu u+V(\varepsilon x)u + \lambda_1 |u|^{2}u + \lambda_2(K\ast|u|^{2})u + \lambda_3|u|^{p-2}u = 0, \;&\text{in}\; \mathbb{R}^{3},\\ \int_{{\mathbb{R}}^3} |u|^{2}dx = a^{2}, \end{array}\right. \end{align*} where $a,\varepsilon>0$, $2 0$ is sufficiently small.