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arXiv · 1109.6773

Stationary solutions of the nonlinear Schr\"odinger equation with fast-decay potentials concentrating around local maxima

Jonathan Di Cosmo·Jean Van Schaftingen
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Abstract

We study positive bound states for the equation $$- \epsilon^2 \Delta u + Vu = u^p, \qquad \text{in $\mathbf{R}^N$}, $$ where $\epsilon > 0$ is a real parameter, $\frac{N}{N-2} < p < \frac{N+2}{N-2}$ 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.

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Jonathan Di Cosmo, Jean Van Schaftingen. 2011-09-30. Stationary solutions of the nonlinear Schr\"odinger equation with fast-decay potentials concentrating around local maxima. https://doi.org/10.1007/s00526-012-0518-z

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