C0-semigroups generated by second order differential operators with general Wentzell boundary conditions

Let us consider the operator (A) over tilde u(x) = phi(x, u'(x))u"(x), where phi is positive and continuous in (0; 1) x R and A is equipped with the so-called generalized Wentzell boundary condition which is of the form a (A) over tilde u + Bu' + cu = 0 at each boundary point, where (a, b, c) not equal (0, 0, 0). This class of boundary conditions strictly includes Dirichlet, Neumann and Robin conditions. Under suitable assumptions on phi, we prove that (A) over tilde generates a positive C-0-semigroup on C[0, 1] and, hence, many previous (linear or nonlinear) results are extended substantially.