The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with magnetic field (1408.3023v1)

Published 13 Aug 2014 in math.AP

Abstract: Based on some ideas introduced by Benci and Cerami \cite{benci-cerami_calvar}, we obtain an abstract result that establishes a version of the Morse relations. Afterward, we use this result to prove multiplicity of solutions for a nonlinear Schr\"odinger equation with an external magnetic field.

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