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arXiv · 1408.3023

The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schr\"odinger equation with magnetic field

Claudianor O. Alves·Rodrigo C. M. Nemer·Sérgio H. M. Soares
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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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Claudianor O. Alves, Rodrigo C. M. Nemer, Sérgio H. M. Soares. 2014-08-13. The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schr\"odinger equation with magnetic field. https://arxiv.org/abs/1408.3023

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