Existence of a ground-state solution for a quasilinear Schrödinger system
| Autor: | Xue Zhang, Jing Zhang |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Frontiers in Physics, Vol 12 (2024) |
| Druh dokumentu: | article |
| ISSN: | 2296-424X |
| DOI: | 10.3389/fphy.2024.1386144 |
| Popis: | In this paper, we consider the following quasilinear Schrödinger system.−Δu+u+k2Δ|u|2u=2αα+β|u|α−2u|v|β,x∈RN,−Δv+v+k2Δ|v|2v=2βα+β|u|α|v|β−2v,x∈RN,where k < 0 is a real constant, α > 1, β > 1, and α + β < 2*. We take advantage of the critical point theorem developed by Jeanjean (Proc. R. Soc. Edinburgh Sect A., 1999, 129: 787–809) and combine it with Pohožaev identity to obtain the existence of a ground-state solution, which is the non-trivial solution with the least possible energy. |
| Databáze: | Directory of Open Access Journals |
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