Exponential decay of solutions to nonlinear elliptic equations with potentials

Reika Fukuizumi*, Tohru Ozawa

*この研究の対応する著者

研究成果: Article査読

10 被引用数 (Scopus)

抄録

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.

本文言語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
6
DOI
出版ステータスPublished - 2005 11月
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)
  • 物理学および天文学(全般)
  • 応用数学

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