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Ground state solutions and geometrically distinct solutions for generalized quasilinear Schrödinger equation
Author(s) -
Li Quanqing,
Teng Kaimin,
Wu Xian
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.4131
Subject(s) - mathematics , ground state , function (biology) , schrödinger equation , state (computer science) , mathematical physics , mathematical analysis , pure mathematics , physics , quantum mechanics , algorithm , evolutionary biology , biology
In this paper, we study the following generalized quasilinear Schrödinger equation− div ( g 2 ( u ) ∇ u ) + g ( u ) g ′ ( u ) | ∇ u | 2 + V ( x ) u = f ( x , u ) , x ∈ R N ,where N ≥3, g : R → R +is a C 1 even function, g (0) = 1 and g ′ ( s ) > 0 for all s > 0. Under some suitable conditions, we prove that the equation has a ground state solution and infinitely many pairs ± u of geometrically distinct solutions. Copyright © 2016 John Wiley & Sons, Ltd.