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- Title
MONOTONICITY PROPERTIES OF THE EIGENVALUES OF NONLOCAL FRACTIONAL OPERATORS AND THEIR APPLICATIONS.
- Authors
BISCI, GIOVANNI MOLICA; SERVADEI, RAFFAELLA; BINLIN ZHANG
- Abstract
In this article we study an equation driven by the nonlocal integrodifferential operator -LK in presence of an asymmetric nonlinear term f. Among the main results of the paper we prove the existence of at least a weak solution for this problem, under suitable assumptions on the asymptotic behavior of the nonlinearity f at 1. Moreover, we show the uniqueness of this solution, under additional requirements on f. We also give a non-existence result for the problem under consideration. All these results were obtained using variational techniques and a monotonicity property of the eigenvalues of -LK with respect to suitable weights, that we prove along the present paper. This monotonicity property is of independent interest and represents the nonlocal counterpart of a famous result obtained by de Figueiredo and Gossez [14] in the setting of uniformly elliptic operators.
- Subjects
EIGENVALUES; ELLIPTIC operators; EIGENFUNCTIONS
- Publication
Electronic Journal of Differential Equations, 2022, p1
- ISSN
1550-6150
- Publication type
Article