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In this paper, we focus on the following M‐coupled system in a bounded domain −Δui+λiui=∑j=1Mκij2qij2*|uj|pij|ui|qij−2ui,y∈Ω,ui∈H01(Ω),i=1,2,…,M, where Ω⊂RN is bounded and pij+qij=2*:=2NN−2(N≥4). By purely variational methods, the existence of ground states… Click to show full abstract
In this paper, we focus on the following M‐coupled system in a bounded domain −Δui+λiui=∑j=1Mκij2qij2*|uj|pij|ui|qij−2ui,y∈Ω,ui∈H01(Ω),i=1,2,…,M, where Ω⊂RN is bounded and pij+qij=2*:=2NN−2(N≥4). By purely variational methods, the existence of ground states to the above system under some assumptions on {λi} and {κij} is proved. Furthermore, we discuss the characterization of the ground states under additional conditions about λi(i=1,2,…,M), and we study the number of the ground states, containing the positive ground states and the semitrivial ground states.
Journal Title: Mathematical Methods in the Applied Sciences
Year Published: 2020
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