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Standing waves for 4‐superlinear Schrödinger–Poisson systems with indefinite potentials
Author(s) -
Liu Shibo,
Wu Yue
Publication year - 2017
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12019
Subject(s) - mathematics , schrödinger's cat , operator (biology) , poisson distribution , space (punctuation) , contrast (vision) , morse theory , morse code , mathematical physics , mathematical analysis , pure mathematics , physics , telecommunications , linguistics , philosophy , repressor , transcription factor , optics , gene , computer science , statistics , biochemistry , chemistry
In this paper we consider 4‐superlinear Schrödinger–Poisson systems. In contrast to most studies, we consider the case where the potential V is indefinite so that the Schrödinger operator − Δ + V possesses a finite‐dimensional negative space. We obtain nontrivial solutions for the problem via Morse theory.