Solvability of some integro-differential equations with the logarithmic Laplacian

We address the existence in the sense of sequences of solutions for a certain integro-differential-type problem involving the logarithmic Laplacian. The argument is based on the fixed point technique when such equation contains the operator without the Fredholm property. It is established that, under the reasonable technical conditions, the convergence in (Formula presented.) of the integral kernels yields the existence and convergence in (Formula presented.) of the solutions. © 2024 Informa UK Limited, trading as Taylor & Francis Group.