Barile, SaraFigueiredo, Giovany M.2022-03-092022-03-092018-10-22Barile, S., & Figueiredo, G. M. (2018). Nontrivial complex solutions for magnetic Schrodinger equations with critical nonlinearities. Electronic Journal of Differential Equations, 2018(174), pp. 1-21.1072-6691https://hdl.handle.net/10877/15470Using minimization arguments we establish the existence of a complex solution to the magnetic Schrödinger equation -(∇ + iA(x))2u + u = ƒ(|u|2)u in ℝN, where N ≥ 3, A:ℝN → ℝN is the magnetic potential and ƒ satisfies some critical growth assumptions. First we obtain bounds from a real Pohozaev manifold. Then relate them to Sobolev imbedding constants and to the least energy level associated with the real equation in absence of the magnetic field (i.e., with A(x) = 0). We also apply the Lions Concentration Compactness Principle to the modula of the minimizing sequences involved.Text21 pages1 file (.pdf)enAttribution 4.0 InternationalMagnetic Schrödinger equationsCritical nonlinearitiesMinimization problemConcentration-compactness methodsPohozaev manifoldArticle