Nonlocal problems with partially integral conditions for different equations of the fourth order sobolev types

Abstract

The report presents results on the solvability of non-local problems with integral conditions with respect to the selected variable t for differential equations ∂2 ∂t2 + a(t) u + b(t)u = f(x, t) ( ) ( is the Laplace operator in spatial variables x1, . . . , xn). The essence of the results is to find sufficient conditions for the existence and uniqueness of regular solutions (i.e. solutions that have all derivatives generalized according to S. L. Sobolev, included in the equation ( )).