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- THOMAS BARTSCH
- Mathematisches Institut, Universität Giessen, Arndtstr. 2, 35392 Giessen, Germany
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- ALEXANDER PANKOV
- Department of Mathematics, Vinnitsa State Pedagogical University, 287100 Vinnitsa, Ukraine
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- ZHI-QIANG WANG
- Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA
書誌事項
- 公開日
- 2001-11
- DOI
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- 10.1142/s0219199701000494
- 公開者
- World Scientific Pub Co Pte Lt
この論文をさがす
説明
<jats:p> We investigate nonlinear Schrödinger equations like the model equation [Formula: see text] where the potential V<jats:sub>λ</jats:sub> has a potential well with bottom independent of the parameter λ > 0. If λ → ∞ the infimum of the essential spectrum of -Δ + V<jats:sub>λ</jats:sub> in L<jats:sup>2</jats:sup>(ℝ<jats:sup>N</jats:sup>) converges towards ∞ and more and more eigenvalues appear below the essential spectrum. We show that as λ→∞ more and more solutions of the nonlinear Schrödinger equation exist. The solutions lie in H<jats:sup>1</jats:sup>(ℝ<jats:sup>N</jats:sup>) and are localized near the bottom of the potential well, but not near local minima of the potential. We also investigate the decay rate of the solutions as |x|→∞ as well as their behaviour as λ→∞. </jats:p>
収録刊行物
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- Communications in Contemporary Mathematics
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Communications in Contemporary Mathematics 03 (04), 549-569, 2001-11
World Scientific Pub Co Pte Lt
