Solvability of nonlinear pseudoparabolic equation with a nonlocal boundary condition Original Research Article

The aim of this paper is to investigate a class of nonlinear pseudo-parabolic equations with a nonlocal condition. We first establish the existence, uniqueness and continuous dependence of a strong generalized solution, by using the energy-integral method. Then, by applying an iterative process based on results obtained for the linear problem, we prove the existence, uniqueness and continuous dependence of the weak generalized solution of the nonlinear problem.