A Proposal on Varational Methods to Elliptic Systems

• Grant number: 22/15812-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2023
• End date: January 20, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Olimpio Hiroshi Miyagaki
• Grantee: Haoyu Li
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

The coupled Schrödinger systems modeling on the phenomenon in the nonlinearoptics become popular topics in the variational methods in recent decades. It describes theinteraction between different particles and the consequences of it. The research on them willnot only improve our understanding on the corresponding mathematical theories, but will alsohelp us to explain the physical phenomena behind them. In this research project, our goalis to investigate carefully and obtain more than just the solvability to the equations and themultiplicity of the solutions. To be precise, we want to obtain the information concerning theshape and the uniqueness of the solutions. We believe this research will develop some newinsight in this research field and benefit a greater scientific research community.

Scientific publications

(5)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

LI, HAOYU; MAIA, BRAULIO B. V.; MIYAGAKI, OLIMPIO H.. Existence of two normalized solutions for a Choquard equation with exponential growth and an L²-subcritical perturbation. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, v. 75, n. 6, p. 19-pg., 2024-12-01. (22/16407-1, 23/09656-8, 22/15812-0)

HUANG, XIAOPENG; LI, HAOYU; WANG, ZHI-QIANG. Multiple non-radial solutions for coupled Schrödinger equations. Journal of Differential Equations, v. 412, p. 22-pg., 2024-08-13. (22/15812-0)

ISHIWATA, MICHINORI; LI, HAOYU. RADIAL SOLUTIONS WITH PRESCRIBED NUMBER OF NODES TO AN ASYMPTOTICALLY LINEAR ELLIPTIC PROBLEM: A PARABOLIC FLOW APPROACH. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 44, n. 6, p. 18-pg., 2024-01-24. (22/15812-0)

ISHIWATA, MICHINORI; LI, HAOYU. Resonant noncooperative elliptic systems via relative morse indices and linking method. Journal of Fixed Point Theory and Applications, v. 26, n. 4, p. 26-pg., 2024-12-01. (22/15812-0)

LI, HAOYU; MIYAGAKI, OLIMPIO HIROSHI. A Liouville-type theorem for the coupled Schrodinger systems and the uniqueness of the sign-changing radial solutions. Journal of Mathematical Analysis and Applications, v. 539, n. 2, p. 11-pg., 2024-07-05. (22/16407-1, 22/15812-0)