Standing waves for nonlinear Hartree type equations: existence and qualitative properties

Autor(es)

Boer, Eduardo ; dos Santos, Ederson Moreira

• Tipo de documento: Artigo Científico
• Fonte: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS; v. 64, n. 5, p. 36-pg., 2025-06-01.

Resumo

We consider systems of the form {-Delta u+u=2pp+q(I alpha & lowast;|v|q)|u|p-2u in RN, -Delta v+v=2qp+q(I alpha & lowast;|u|p)|v|q-2v in RN, for alpha is an element of(0,N), max{2 alpha/N,1}<p,q<2 & lowast; and 2(N+alpha)/N<p+q<2(alpha)(& lowast;), where I alpha denotes the Riesz potential, 2 & lowast;={2N/N-2 for N >= 3, +infinity for N=1,2, and2 alpha & lowast;={2(N+alpha)/N-2 for N >= 3, +infinity for N=1,2. This type of systems arises in the study of standing wave solutions for a certain approximation of the Hartree theory for a two-component attractive interaction. We prove existence and some qualitative properties for ground state solutions, such as definite sign for each component, radial symmetry and sharp asymptotic decay at infinity, and a regularity/integrability result for the (weak) solutions. Moreover, we show that the straight lines p+q=2(N+alpha)/N and p+q=2(alpha)(& lowast;) are critical for the existence of solutions. (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: 23/05445-2 - Algumas classes de sistemas de Choquard-Schrödinger: Existência, multiplicidade e propriedades de soluções
• Beneficiário: Eduardo de Souza Böer
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado