October 2, 2025Open Access

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

Puntos clave

Multiple normalized solutions exist for the dipolar gross-pitaveskii equation in R^3, indicating complex dynamics.
The number of normalized solutions corresponds to the number of global minimum points of the external potential.
Variational methods are employed to establish the results under specific conditions on the external potential.
The findings imply significant behaviors related to perturbations and potentials in mathematical physics.

Resumen

In this paper, we study the existence of multiple normalized solutions to the following dipolar Gross-Pitaveskii equation with a mass subcritical perturbation align* \ array{lll -12Δu+μu+V (x) u + λ₁ |u|^2u + λ₂ (K|u|^2) u + λ₃|u|^p-2u = 0, \; R^3, \\ ₑ℃ |u|^2dx = a^2, array. align* where a, >0, 2 0 is sufficiently small.

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