Well-posed problem of nonlinear singular distributed parameter systems and nonlinear GE-semigroup

According to the well-posed problem of nonlinear singular distributed parameter systems, frst of all, the nonlinear GE-semigroup induced by a continuous(possibly nonlinear) operator is introduced in Banach space, which is a generalization of GE-semigroup(i.e., generalized operator semigroup), and the properties of nonlinear GE-semigroup are discussed; and then the existence, uniqueness and constructive expression for the strong solution of nonlinear singular distributed parameter system are discussed by nonlinear GE-semigroup; at last, the exponential stability of nonlinear singular distributed parameter system is studied by using nonlinear GE-semigroup, functional analysis and operator theory in Banach space.