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Ground state solutions for a generalized quasilinear Choquard equation
Author(s) -
Zhang Jing,
Ji Chao
Publication year - 2021
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.7169
Subject(s) - mathematics , riesz potential , ground state , mathematical analysis , energy method , energy (signal processing) , state (computer science) , variational method , physics , quantum mechanics , algorithm , statistics
This paper is concerned with the following quasilinear Choquard equation:− Δ u + V ( x ) u − u Δ ( u 2 ) = ( I α ∗ G ( u ) ) g ( u ) ,x ∈ ℝ N , where N ≥ 3 , 0 < α < N , V :ℝ N → ℝ is radial potential, G ( t ) = ∫ 0 t g ( s ) d s , and I α is a Riesz potential. Using the variational method we establish the existence of ground state solutions under appropriate assumptions, that is, nontrivial solution with least possible energy.