Exponential decay of solutions to nonlinear elliptic equations with potentials

Reika Fukuizumi, Tohru Ozawa

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

Exponential decay estimates are obtained for complex-valued solutions to nonlinear elliptic equations in ℝn, where the linear term is given by Schrödinger operators H = - Δ + V with nonnegative potentials V and the nonlinear term is given by a single power with subcritical Sobolev exponent in the attractive case. We describe specific rates of decay in terms of V, some of which are shown to be optimal. Moreover, our estimates provide a unified understanding of two distinct cases in the available literature, namely, the vanishing potential case V = 0 and the harmonic potential case V(x) = |x|2.

Original languageEnglish
Pages (from-to)1000-1011
Number of pages12
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume56
Issue number6
DOIs
Publication statusPublished - 2005 Nov 1

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Keywords

  • Bound states
  • Exponential decay
  • Nonlinear elliptic equations

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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