Abstract: This work investigates the solvability of nonlocal boundary value problems for the generalized Boussinesq–Love differential equation [1–3] 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.

Cite: Kozhanov A.I. , Wang M.
Nonlocal problems for the generalized Boussinesq–Love equation
Russian-Chinese Conference "Differential and Difference Equations" 31 Oct - 6 Nov 2025