Work

A weighted eigenvalue problem for mixed local and nonlocal operators with potential

Year: 2025

Type: article

Abstract: We study an indefinite weighted eigenvalue problem for an operator of mixed‐type (that includes both the classical ‐Laplacian and the fractional ‐Laplacian ) in a bounded open subset with Lipschitz boundary , which is given by where is a parameter, exponents , and for with a.e. in . Using the variational tools together with a weak comparison and strong maximum principles , we investigate the existence and uniqueness of principal eigenvalue and discuss its qualitative properties. Moreover, with the help of Ljusternik–Schnirelman category theory , it is proved that there exists a nondecreasing sequence of positive eigenvalues , which goes to infinity. Further, we show that the set of all positive eigenvalues is closed , and eigenfunctions associated with every positive eigenvalue are bounded.

Source: Mathematische Nachrichten

DOI: 10.1002/mana.70093

Authors: Radhakrishnan Lakshmi, Ratan Kr. Giri, Sekhar Ghosh

Institutions: National Institute of Technology Calicut, LNM Institute of Information Technology

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Department of Science and Technology, Ministry of Science and Technology, India, Ministry of Education, India

Awards: G3121417047, G3410714353