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Existence and multiplicity of systems of Kirchhoff‐type equations with general potentials
Author(s) -
Che Guofeng,
Chen Haibo
Publication year - 2017
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.4007
Subject(s) - mathematics , multiplicity (mathematics) , type (biology) , morse code , morse theory , pure mathematics , mathematical analysis , ecology , biology , electrical engineering , engineering
This paper is concerned with the following systems of Kirchhoff‐type equations:− a + b ∫R N| ∇ u | 2 dx Δ u + V ( x ) u = F u ( x , u , v ) , x ∈ R N ,− c + d ∫R N| ∇ v | 2 dx Δ v + V ( x ) v = F v ( x , u , v ) , x ∈ R N ,u ( x ) → 0 ,v ( x ) → 0as | x | → ∞ .Under more relaxed assumptions on V ( x ) and F ( x , u , v ), we first prove the existence of at least two nontrivial solutions for the aforementioned system by using Morse theory in combination with local linking arguments. Then by using the Clark theorem, the existence results of at least 2 k distinct pairs of solutions are obtained. Some recent results from the literature are extended. Copyright © 2016 John Wiley & Sons, Ltd.