Second-order differential operators with integral boundary conditions and generation of analytic semigroups

Consider a second-order differential operator Lu. = u " + q(1)(x)u' + q(0)(x)u with integral boundary conditions of the form (a)integral R-b(i)(t)u(t)dt + (a)integral S-b(i)(t)u'(t)dt = 0, i = 1,2. We study sufficient conditions on the functions R-i and S-i, i = 1,2, such that the operator L is the generator of an analytic semigroup of operators on L-p(a, b). The generation of analytic semigroups is proved by showing the estimate \\R(lambda :L)\\ less than or equal to M/\lambda\ for the resolvent operator in st suitable sector of the complex plane. The motivation for this work is to generalize the results in [3], where nonseparated boundary conditions were considered.