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

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

2011-09-30

arxiv.org/abs/1109.6773v2

Mathematics

Analysis of PDEs

25 pages, incorporated suggestions by the referee

Scientific paper

We study positive bound states for the equation {equation*} - \epsilon^2 \Delta u + Vu = u^p, \qquad \text{in (\mathbf{R}^N)}, {equation*} 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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