In this paper we give a multiplicity result for the following Chern-Simons-Schrödinger equationwhere hu(s) = s 0 τ u 2 (τ ) dτ , under very general assumptions on the nonlinearity g. In particular, for every n ∈ N, we prove the existence of (at least) n distinct solutions, for every q ∈ (0, qn), for a suitable qn.
This paper deals with the Klein-Gordon-Maxwell system when the nonlinearity exhibits critical growth. We prove the existence of positive ground state solutions for this system when a periodic potential V is introduced. The method combines the minimization of the corresponding Euler-Lagrange functional on the Nehari manifold with the Brézis and Nirenberg technique.
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