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 (SMλ), while for λ>0 large enough, a recent Ricceri-type result guarantees the existence of at least two non-trivial solutions for (SMλ) as well as the 'stability' of system (SMλ) with respect to an arbitrary subcritical perturbation of the Schrödinger equation.
- SchrödingerMaxwell system
ASJC Scopus subject areas
- Economics, Econometrics and Finance(all)
- Computational Mathematics
- Applied Mathematics