The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schr\"odinger equation with magnetic field
Abstract
Based on some ideas introduced by Benci and Cerami benci-ceramicalvar, 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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