Nonlinear scalar field equation with point interaction
Analysis of PDEs
2025-09-15 v3
Abstract
This paper is devoted to the study of the nonlinear scalar field equation with a point interaction at the origin in dimensions two and three. By applying the mountain pass theorem and the technique of adding one dimensional space, we prove the existence of a nontrivial singular solution for a wide class of nonlinearities. We also establish the Pohozaev identity by proving a pointwise estimate of the gradient near the origin. Some qualitative properties of nontrivial solutions are also given.
Cite
@article{arxiv.2410.00189,
title = {Nonlinear scalar field equation with point interaction},
author = {Alessio Pomponio and Tatsuya Watanabe},
journal= {arXiv preprint arXiv:2410.00189},
year = {2025}
}