## Taiwanese Journal of Mathematics

### Strict Monotonicity and Unique Continuation for General Non-local Eigenvalue Problems

#### Abstract

We consider the weighted eigenvalue problem for a general non-local pseudo-differential operator, depending on a bounded weight function. For such problem, we prove that strict (decreasing) monotonicity of the eigenvalues with respect to the weight function is equivalent to the unique continuation property of eigenfunctions. In addition, we discuss some unique continuation results for the special case of the fractional Laplacian.

#### Article information

Source
Taiwanese J. Math., Volume 24, Number 3 (2020), 681-694.

Dates
Revised: 2 July 2019
Accepted: 30 July 2019
First available in Project Euclid: 19 May 2020

https://projecteuclid.org/euclid.twjm/1589875224

Digital Object Identifier
doi:10.11650/tjm/190709

#### Citation

Frassu, Silvia; Iannizzotto, Antonio. Strict Monotonicity and Unique Continuation for General Non-local Eigenvalue Problems. Taiwanese J. Math. 24 (2020), no. 3, 681--694. doi:10.11650/tjm/190709. https://projecteuclid.org/euclid.twjm/1589875224

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