Existence of Solutions for a Class of Integro-Differential Equations With the Logarithmic Laplacian and Transport

In this paper, we consider an integro-differential equation in \(L^2(\mathbb {R})\) $L^2(\mathbb{R})$ , which involves the logarithmic Laplacian in the presence of a drift term. The linear operator associated with the problem has the Fredholm property. By using a fixed point technique, we establish the existence of solutions.