Dynamical Systems Method (dsm) for Unbounded Operators
نویسندگان
چکیده
Let L be an unbounded linear operator in a real Hilbert space H, a generator of a C0 semigroup, and let g : H → H be a C2 loc nonlinear map. The DSM (dynamical systems method) for solving equation F (v) := Lv+ g(v) = 0 consists of solving the Cauchy problem u̇ = Φ(t, u), u(0) = u0, where Φ is a suitable operator, and proving that i) ∃u(t) ∀t > 0, ii) ∃u(∞), and iii) F (u(∞)) = 0. Conditions on L and g are given which allow one to choose Φ such that i), ii), and iii) hold.
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