Work

Uniqueness and nondegeneracy of ground states for 2d-nonlinear scalar field equations with point interaction

Year: 2025

Type: article

Abstract: We study uniqueness and nondegeneracy of action ground states for nonlinear scalar field equations in two dimensions with a point interaction at the origin. It is known that the all ground states are radial, positive, and decreasing functions. In this paper we prove the uniqueness of positive radial solutions by a method of Pohožaev identities. As a corollary, we obtain the uniqueness of ground states. Moreover, by a variational and ODE technique, we show that the ground state is a nondegenerate critical point of the action in the energy space.

Source: Nonlinear Differential Equations and Applications NoDEA

DOI: 10.1007/s00030-025-01137-4

Author: Noriyoshi Fukaya

Institutions: Waseda University, Tsuda University, Osaka Metropolitan University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Japan Society for the Promotion of Science