A perturbation method for k-mixtures of Bose-Einstein condensates

作者：Yue Xiaorui; Zou Wenming

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2015, 66(3): 1023-1035.

DOI：10.1007/s00033-014-0468-8

• Multiple mixed states of nodal solutions
• Bose-Einstein condensates systems
• Perturbation method

Consider the equations as below which is regarded the Bose-Einstein condensates system:
(P){-Delta u(j) + lambda(j)u(j) = mu(j)u(j)(3) + Sigma(i not equal j) beta(ij)u(i)(2)u(j), x is an element of Omega, u(j) = 0 on partial derivative Omega, j=1,...,k,
where Omega is a bounded smooth domain in ; for is the first eigenvalue of -I" with the Dirichlet boundary condition; mu (j) > 0 for is small and beta (ij) = beta (ji) for . We develop an abstract perturbation method to obtain prescribed number of mixed states of nodal solutions and then apply it to the above Bose-Einstein condensates systems. Besides, by using such a method, we also get a positive solution for problem () under the same conditions.

• 出版日期2015-6
• 单位清华大学