A direct method of moving planes for logarithmic Schrödinger operator
Rong Zhang
Chinese Academy of Sciences, Beijing, P. R. China; Ghent University, Ghent, BelgiumVishvesh Kumar
Ghent University, Ghent, BelgiumMichael Ruzhansky
Ghent University, Ghent, Belgium; Queen Mary University of London, London, UK
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Abstract
In this paper, we study the radial symmetry and monotonicity of nonnegative solutions to nonlinear equations involving the logarithmic Schrödinger operator corresponding to the logarithmic symbol , which is a singular integral operator given by
where , and is the modified Bessel function of the second kind with index . The proof hinges on a direct method of moving planes for the logarithmic Schrödinger operator.
Cite this article
Rong Zhang, Vishvesh Kumar, Michael Ruzhansky, A direct method of moving planes for logarithmic Schrödinger operator. Z. Anal. Anwend. (2024), published online first
DOI 10.4171/ZAA/1757