Abstract: | We consider the evolution equation whose right-hand side is the sum of a linear unbounded operator generating a compact strongly
continuous semigroup and a continuous operator acting in function spaces. We prove the existence of a solution that stays
within a given closed convex set and moreover, satisfies a functional boundary condition, particular cases of which are the
Cauchy initial condition, periodicity condition, mixed condition including continuous transformations of spatial variables,
etc. The main result is illustrated by using an example of the boundary-value problem for a partial operator-differential
equation.
Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 48–60, January, 1999. |