Ngày tải lên :
20/06/2014, 22:20
... Hamiltonian systems, wave equations, and Schrödinger equations Theorem 3.2 Assume that F(t, x) satisfies (A’), (B1), (B3), and (B4) and the following assumption: (B5) T + F(t, 0)dt = 0, and there ... positive constants ε and δ such that < ε < C1 and < δ < ε, where C1 is the same as in (3.3), and |F(t, x)| ≤ (M + ε)|x|r1 (3:15) for a.e t Î [0, T] and |x| ≤ δ Let s:= δ/C1 and ||u|| = s, since ... u Î Lp(t) and v Î Lq(t), we have T uvdt ≤ 2|u|p(t) |v|q(t) , 1 + = p(t) q(t) (ii) If p (t) and p (t) Î C([0, T], ℝ + ) and p (t) ≤ p (t) for any t Î [0, T], then Lp2 (t) → Lp1 (t), and the embedding...