Work

Complex and Real Valued Solutions for Fractional Helmholtz Equation

Year: 2025

Type: article

Abstract: ABSTRACT In this paper, we are concerned with the limiting absorption principle for the fractional Helmholtz equation: , where and are two real parameters. By establishing the boundedness estimate for the resolvent of fractional Helmholtz operator, we obtain the nontrivial complex valued solutions for the fractional Helmholtz equation. By setting up a dual variational framework, we also obtain the real valued solutions for the fractional Helmholtz equation via a non‐vanishing principle.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.11197

Authors: Zifei Shen, Shuijin Zhang

Institutions: Zhejiang Normal University, Gannan Normal University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $5,000

Funder: National Natural Science Foundation of China