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Characterization of ground states for an M‐coupled system in a bounded domain with critical exponent
Author(s) -
He Qihan,
Yang Jing
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6429
Subject(s) - bounded function , ground state , mathematics , domain (mathematical analysis) , characterization (materials science) , exponent , critical exponent , mathematical analysis , pure mathematics , physics , geometry , quantum mechanics , scaling , linguistics , philosophy , optics
In this paper, we focus on the following M‐coupled system in a bounded domain− Δ u i + λ iu i =∑ j = 1 Mκ i j2 q i j2 *| u j|p i j| u i|q i j − 2u i , y ∈ Ω ,u i ∈ H 0 1 ( Ω ) , i = 1 , 2 , … , M ,where Ω ⊂ R Nis bounded andp i j + q i j = 2 * : = 2 N N − 2 ( N ≥ 4 ) . By purely variational methods, the existence of ground states to the above system under some assumptions on { λ i } and { κ i j } is proved. Furthermore, we discuss the characterization of the ground states under additional conditions about λ i ( i =1,2,…, M ), and we study the number of the ground states, containing the positive ground states and the semitrivial ground states.