Weakly monotone decreasing solutions to elliptic Schrodinger integral system

Authors

  • Edward Chernysh McGill Univ., Montreal, QC, Canada

DOI:

https://doi.org/10.58997/ejde.2021.28

Keywords:

Elliptic Schrodinger system; poly-harmonic equation; a priori decay estimate; weakly monotone decreasing solution

Abstract

In this article, we study positive solutions to an elliptic Schrodinger system in \(R^n\) for \(n\geq 2\). We give general conditions guaranteeing the non-existence of positive solutions and introduce weakly monotone decreasing functions. We also establish lower-bounds on the decay rates of positive solutions and obtain upper-bounds when these are weakly monotone decreasing.

For more information see https://ejde.math.txstate.edu/Volumes/2021/28/abstr.html

References

Li, Y.; Asymptotic behavior of positive solutions of equation ∆u + K(x)up = 0 in Rn. J. Differential Equations 95 (1992) no. 2, 304-330.

Liu, B.; Ma, L.; Symmetry results for decay solutions of elliptic systems in the whole space, Adv. Math. 225 (2010), no. 6, 30523063.

Vetois, Jerˆome; Decay Estimates and Symmetry of Finite Energy Solutions to Elliptic Sys- tems in Rn. Indiana University Mathematics Journal 68 (2019), no. 3, 663-696.

Villavert, John; Qualitative properties of solutions for an integral system related to the Hardy- Sobolev inequality. J. Differential Equations 258 (2015) no. 5, 1685-1714.

Villavert, John; Sharp existence criteria for positive solutions of Hardy-Sobolev type systems. Commun. Pure Appl. Anal. 14 (2) (2015) 493-515.

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Published

2021-04-13

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How to Cite

Weakly monotone decreasing solutions to elliptic Schrodinger integral system. (2021). Electronic Journal of Differential Equations, 2021(01-104), No, 28, 1-11. https://doi.org/10.58997/ejde.2021.28