Year: 2024
Type: article
Abstract: We are concerned with the study of positive solutions to the integral equation$ u(x) = \int\limits_{ \mathbb R^N}\frac{K(y) u(y)^{-p}}{|x-y|^{N-\alpha}} dy\quad\mbox{ in } \mathbb R^N (N\geq 1), $where $ p>0 $, $ \alpha\in (0, N) $ and $ K\in C(0, \infty) $ is a positive and continuous function which satisfies $ C_1(1+|x|)^{-\beta}\leq K(x)\leq C_2(1+|x|)^{-\beta} $ in $ \mathbb R^N $, for some $ \beta>0 $ and $ C_2>C_1>0 $. We discuss the existence, uniqueness, and asymptotic behaviour of solutions to the above equation in terms of $ \alpha, \beta $ and $ p $. Solutions with finite and infinite total mass are also considered.
Authors: Marius Ghergu, Changhong Li
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Science Foundation Ireland
OpenAlex ID: W4404612929