An upper bound for the least energy of a sign-changing solution to a zero mass problem

Autor: Clapp Mónica, Maia Liliane, Pellacci Benedetta
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Advanced Nonlinear Studies, Vol 24, Iss 2, Pp 463-476 (2024)
Druh dokumentu: article
ISSN: 2169-0375
2022-0065
DOI: 10.1515/ans-2022-0065
Popis: We give an upper bound for the least possible energy of a sign-changing solution to the nonlinear scalar field equation −Δu=f(u),u∈D1,2(RN), $-{\Delta}u=f\left(u\right), u\in {D}^{1,2}\left({\mathrm{R}}^{N}\right),$ where N ≥ 5 and the nonlinearity f is subcritical at infinity and supercritical near the origin. More precisely, we establish the existence of a nonradial sign-changing solution whose energy is smaller that 12c 0 if N = 5, 6 and smaller than 10c 0 if N ≥ 7, where c 0 is the ground state energy.
Databáze: Directory of Open Access Journals