Stationary solutions of the nonlinear Schrödinger equation with fast-decay potentials concentrating around local maxima

Di Cosmo, J.;Van Schaftingen, Jean
(2013) Calculus of Variations and Partial Differential Equations — Vol. 47, n° 1-2, p. 243-271 (2013)

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Abstract
We study positive bound states for the equation -ε2 Δu + Vu = up, in ℝN, where ε > 0 is a real parameter, and V is a nonnegative potential. Using purely variational techniques, we find solutions which concentrate at local maxima of the potential V without any restriction on the potential. © 2012 Springer-Verlag.
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Di Cosmo, J., & Van Schaftingen, J. (2013). Stationary solutions of the nonlinear Schrödinger equation with fast-decay potentials concentrating around local maxima. Calculus of Variations and Partial Differential Equations, 47(1-2), 243-271. https://doi.org/10.1007/s00526-012-0518-z (Original work published 2013)