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Uniqueness results for noncoercive nonlinear elliptic equations with two lower order terms
Existence of unstable standing waves for the inhomogeneous nonlinear Schrödinger equation
| 1. | Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408 |
$i u_t + \Delta u + V(\epsilon x ) |u|^{p-1} u = 0, \quad x \in \mathbf R^n$
with the critical power $ p = 1 + 4/n, n \ge 2, $ under certain conditions on the inhomogeneous term $ V $ with a small $ \epsilon > 0. $ We also demonstrate that these localized standing-waves converge to standing waves of the nonlinear Schrödinger equation with the homogeneous nonlinearity.
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