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Multiple positive solutions for a nonlinear Schrödinger equation

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Abstract.

We are interested in positive entire solutions of the nonlinear Schrödinger equation \(-\Delta u+(\lambda a(x)+1)u = u^p\) where a? 0 has a potential well and p > 1 is subcritical. Using variational methods we prove the existence of multiple positive solutions which localize near the potential well int(a -1(0)) for \(\lambda\) large.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Giessen, Arndtstr. 2, 35392 Giessen, Germany, , , , , , DE

    Th. BartschRID="*"

  2. Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA, , , , , , US

    Z.-Q. WangRID="*"ID="*"Research supported by NATO grant CRG 970179 and DFG grant Gi 30/68-1

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  1. Th. BartschRID="*"
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  2. Z.-Q. WangRID="*"ID="*"Research supported by NATO grant CRG 970179 and DFG grant Gi 30/68-1
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Received: November 21, 1998

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ID="*"Research supported by NATO grant CRG 970179 and DFG grant Gi 30/68-1

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BartschRID="*", T., WangRID="*"ID="*"Research supported by NATO grant CRG 970179 and DFG grant Gi 30/68-1, ZQ. Multiple positive solutions for a nonlinear Schrödinger equation. Z. angew. Math. Phys. 51, 366–384 (2000). https://doi.org/10.1007/PL00001511

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  • DOI: https://doi.org/10.1007/PL00001511

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