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Liouville Theorem for Indefinite Fractional Parabolic Equation Involving Pseudo-relativistic Schrödinger Operators

Year: 2025

Type: article

Abstract: In this paper, we study the following indefinite fractional parabolic equation involving pseudo-relativistic Schrödinger operators $\begin{equation*}\frac{\partial u}{\partial t}(x, t)+(-\Delta+m^2)^su(x, t)=a(x_1)f(u(x, t)), \ \ \mbox{in}\ { \mathbb R^N}\times\mathbb R, \end{equation*}$ where $0 and the mass $m>0$ . We first prove the monotonicity of positive bounded solutions by using the method of moving planes. Moreover, the nonexistence of positive bounded solutions is established.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20250044

Authors: Guangwei Du, Fushan Li, Yuying Zheng

Institution: Qufu Normal University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4411533891

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