Qualitative properties for solutions of problems involving elliptic equations
Computing qualitatively correct approximations of partial differential equations i...
Well-posedness and qualitative properties for nonlinear PDEs
| Full text | |
| Author(s): |
Boer, Eduardo
;
dos Santos, Ederson Moreira
Total Authors: 2
|
| Document type: | Journal article |
| Source: | CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS; v. 64, n. 5, p. 36-pg., 2025-06-01. |
| Abstract | |
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) | |
| FAPESP's process: | 22/16407-1 - TESdE: Thematic on Equations and Systems of differential Equations |
| Grantee: | Ederson Moreira dos Santos |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 23/05445-2 - Some classes of Choquard-Schrödinger systems: Existence, multiplicity and properties of solutions |
| Grantee: | Eduardo de Souza Böer |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |