On the SchrödingerMaxwell system involving sublinear terms

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Abstract

In this paper, we study the coupled SchrödingerMaxwell system -Δu+u+eφu=λα(x)f(u)inR3,-Δφ= 4πeu2inR3, where e>0, α∈L∞(R3)∩L6(5-q)( R3) for some q∈(0,1), and the continuous function f:R→R is superlinear at zero and sublinear at infinity, e.g., f(s)=min(| s|r,|s|p) with 0<r<1<p. First, for small values of λ>0, we prove a non-existence result for (S), while for λ>0 large enough, a recent Ricceri-type result guarantees the existence of at least two non-trivial solutions for (S) as well as the 'stability' of system (S) with respect to an arbitrary subcritical perturbation of the Schrödinger equation.

Original languageEnglish
Pages (from-to)213-223
Number of pages11
JournalNonlinear Analysis: Real World Applications
Volume13
Issue number1
DOIs
Publication statusPublished - Feb 1 2012

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Keywords

  • Multiplicity
  • Non-existence
  • SchrödingerMaxwell system
  • Stability
  • Sublinearity

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics

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