Work

Liouville theorems for the static Schrodinger equations with van der Waals type potentials

Year: 2025

Type: article

Abstract: In this article, we are concerned with the static Schrödinger equation with the van der Waals potential. Such an equation can be transformed into a system of integral equations. We present the nonexistence of two classes of positive solutions. One is a class of locally bounded positive super-solutions, and the other is a class of positive solutions with some integrability. To prove the nonexistence of positive integrable solutions, we investigate their qualitative properties, involving the radial symmetry, the better integrability, the differentiability, and the decay estimates at infinity. Here, the regularity lifting lemma, the method of moving planes in integral forms, and the Pohozaev identity in integral forms play important roles.

Source: Canadian Journal of Mathematics

DOI: 10.4153/s0008414x25101776

Authors: Tiantian Zhou, Yutian Lei

Institution: Nanjing Normal University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Government of Jiangsu Province, Natural Science Foundation of Jiangsu Province

Award: G8188947746