Premium
Existence and multiplicity results for the nonlinear Schrödinger–Maxwell systems
Author(s) -
Chen Huiwen,
He Zhimin
Publication year - 2015
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.3420
Subject(s) - mathematics , multiplicity (mathematics) , nonlinear system , schrödinger's cat , simple (philosophy) , mathematical physics , maxwell's equations , critical point (mathematics) , sign (mathematics) , mathematical analysis , quantum mechanics , physics , philosophy , epistemology
In this paper, we study the nonlinear Schrödinger–Maxwell system where the potential V and the primitive of g are allowed to be sign‐changing, and g is local superlinear. Under some simple assumptions on V , Q and g , we establish some existence criteria to guarantee that the aforementioned system has at least one nontrivial solution or infinitely many nontrivial solutions by using critical point theory. Recent results in the literature are generalized and significantly improved. Copyright © 2015 John Wiley & Sons, Ltd.