Dynamical systems method and surjectivity of nonlinear maps

摘要

If F: H → H is a C_(loc)~2-map in a real Hilbert space, sup~u ε B(u_0, R)‖[F'(u)]~(-1) ‖ ≤ m(R), and lim sup_(R>0) R/( m(R)) = ∞, then F is surjective.