Functional differential equations and nonlinear semigroups in Lp-spaces

AbstractThe autonomous nonlinear functional differential equation x(t) = F(xt), t ⩾ 0, x0 = φ is studied as a semigroup of nonlinear operators in Lp function spaces. The method employed is to construct a semigroup of nonlinear operators which may be associated with the solutions of this equation. New existence and stability results are obtained for this equation by means of the semigroup approach