A Liouville-type theorem for the coupled Schrodinger systems and the uniqueness of the sign-changing radial solutions

Autor(es)

Li, Haoyu ; Miyagaki, Olimpio Hiroshi

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 539, n. 2, p. 11-pg., 2024-07-05.

Resumo

In this paper, we study the sign-changing radial solutions of the following coupled Schrodinger system {-Delta u(j) + lambda(j)u(j) = mu(j)u(j)(3) + Sigma(i not equal j) beta(ij)u(i)(2)u(j) in B-1, u(j) is an element of H-0,1(r)(B-1) for j = 1, ..., N. Here, lambda(j), mu(j) > 0 and beta(ij)= beta(ji) are constants for i, j = 1, ..., N and i not equal j. B-1 denotes the unit ball in the Euclidean space R-3 centred at the origin. For any P-1, ..., P-N is an element of N, we prove the uniqueness of the radial solution (u(1), ..., u(j)) with u(j) changes its sign exactly P-j times for any j = 1, ..., N in the following case: lambda(j) >= 1 and vertical bar beta(ij)vertical bar are small for i, j = 1, ..., N and i not equal j. New Liouville-type theorems and boundedness results are established for this purpose. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. (AU)

• Processo FAPESP: 22/16407-1 - TESEd: Temático em Equações e Sistemas de Equações diferenciais
• Beneficiário: Ederson Moreira dos Santos
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 22/15812-0 - Uma proposta sobre o metodo variacional para um sistema eliptico.
• Beneficiário: Haoyu Li
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado