Year: 2023
Type: preprint
Abstract: We let $\Omega$ be a bounded domain of $\mathbb{R}^3$ and $\Gamma$ be a closed curve contained in $\Omega$. We study existence of positive solutions $u \in H^1_0\left(\Omega\right)$ to the equation where $h$ is a continuous function and $\rho_\Gamma$ is the distance function to $\Gamma$. We prove existence of solutions depending on the regular part of the Green function of linear operator. We prove the existence of positive mountain pass solutions for this Euler-Lagrange equation depending on the mass which is the regular part of the Green function of the linear operator $-\Delta+h$. AMS Mathematics Subject Classification: 35J08, 35A23, 35J60.
Source: Research Square
Author: El Hadji Abdoulaye THIAM
Institution: Université de Thiès
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4388909413