대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제61권2호
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  • Pages.541-556
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  • 2024
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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QUASILINEAR SCHRÖDINGER EQUATIONS FOR THE HEISENBERG FERROMAGNETIC SPIN CHAIN

  • Yongkuan Cheng (School of Mathematics South China University of Technology) ;
  • Yaotian Shen (School of Mathematics South China University of Technology)
  • 투고 : 2023.04.11
  • 심사 : 2023.11.14
  • 발행 : 2024.03.31
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초록

In this paper, we consider a model problem arising from a classical planar Heisenberg ferromagnetic spin chain $-{\Delta}u+V(x)u-{\frac{u}{\sqrt{1-u^2}}}{\Delta}{\sqrt{1-u^2}}={\lambda}{\mid}u{\mid}^{p-2}u$, x ∈ ℝN, where 2 ≤ p < 2*, N ≥ 3. By the Ekeland variational principle, the cut off technique, the change of variables and the L∞ estimate, we study the existence of positive solutions. Here, we construct the L∞ estimate of the solution in an entirely different way. Particularly, all the constants in the expression of this estimate are so well known.

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과제정보

This work was financially supported by NSFC (No. 12271179), the Guangdong Basic and Applied Basic Research Foundation (No. 2020A1515010338).

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