Exponential decay of solutions to nonlinear elliptic equations with potentials

Reika Fukuizumi, Tohru Ozawa

研究成果: Article

10 引用 (Scopus)

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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.

元の言語English
ページ(範囲)1000-1011
ページ数12
ジャーナルZeitschrift fur Angewandte Mathematik und Physik
56
発行部数6
DOI
出版物ステータスPublished - 2005 11 1

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ASJC Scopus subject areas

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

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