Abstract:

This work investigates the solvability of nonlocal boundary value problems for the generalized Boussinesq-Love differential equation in anisotropic S.L. Sobolev spaces. A distinctive feature of the studied problems is that their nonlocal conditions represent Samarskii-Ionkin type conditions with respect to the temporal (distinguished) variable. The main objective of this work is to prove existence and uniqueness theorems for regular solutions of the considered problems -- specifically, solutions possessing all generalized derivatives in the S.L. Sobolev sense that appear in the corresponding equation.