Книги по разным темам
1 R f(p,t) R = K G, 1 K G K G K K K = G = G УG = K G.u :G R K G u(p) K m = infЦu : u = u(p),p K, M = supЦu : u = u(p),p K.
m M. K K K u(p) inf sup min max 1 F = K Цp G : u(p) M = u(p) = K Цp G : u(p) M, R E = Цp G : u(p) > M. p G m u(p) M u(p) > M K K Цp G : u(p) > M =, 11 f(p,t)G t F = K Цp G : u(p) m = = K Цp G : u(p) m u(t) u(f(p,t)), t. E = Цp G : u(p) < m. u 11 E = f(p,t)G пpи t, f(p,t) f(p,t)G пpи < t <, p u(t) D+(p) =. ecли s < t, тo u(s) < u(t). f(p,t) F = K Цp G : m u(p) M = C t = t(C), = K Цp G : m u(p) M.
f(p,t) C t(C) < t < +. 1 1 R = F E, 1 1 F E F C0 E E tk + f(p,tk)C F : E = R У F E = G У F qk f(p,tk) F F C0 F = E = E У E = F E qk r0 tk + j j f(p,tk ) qk r0 r0 j j f(p,t) E = Цp G : u(p) < m Цp G : u(p) > M, r0 D+(p) 1 1 1 D+(p) q0 p G u(p) < m f(p,t) Цp G : u(p) < m =, tk + f(p,tk) q 11 pk f(p,tk) C0 = Цp1,Е,pk,Е;q C0 1 f(p,tk)C0 k = 1,2,Е = u(p) > M p1 F C0 p1 E p1 G 1 u(p1) p1 G p1 F m u(p1) M p F u(p) > M u(p1) M p1 G p1 G УG = K f(p,t) F 0 t < + m u(p1) M f(p,t) u(p1) M u(p1) M p F u(p) < m f(p,t) F - < t 0 M < u(0) < u(t1) M.
f(p,t) f(p,t) F p F p K 0 t < + p G u u(t) u(f(p,t)) t 0 G G u(p) t + p F u(p) [mM], u(p) > M u(p) < m f(p,t), 0 t < + q R 1 tk + p E pk f(p,tk) q.
u(p) > M f(p,t) E 0 t < + u(tk) = u(f(p,tk)) = u(pk) u(q) = c p E u(p) < m u(t) t + f(p,t)E - < t 0.
c M < u(0) < u(t) < c 0 < t < + 1 pk q f(pk,t) f(q,t) oкaльнo пpи - < t < +, T t 0 f(p,t)F p F p E E u(f(q,t)) = lim u(f(pk,t)) = lim u(f(f(p,tk),t)) = f(p,t) t k+ k+ > 0 f(p,t) E = lim u(f(p,t + tk)) = lim u(t + tk) = c, k+ k+ | t |< f(p,t) F | t |< t f(q,t) T t1 t u(r) = c > M T t1 v(t) u(f(q,t)) = c v(t) f(p,t) F пpи 0 t < t1; p1 f(p,t1)F.
G E = 0 = t1 f(q,t) E p = f(p,0) F p E v(t) p E f(p,t) E 0 t < t1 p1 = f(p,t1) M G E 1 f(p,t) u(t) u(f(p,t)) 0 t t1 p F 0 t < + u(0) = u(f(p,0)) = p F u(p) > M f(p,t) F npu 0 t < +, t = t1 < 0 t1 0 f(p,t) F - < t < t1 f(p,t) F npu 0 t t1, f(p,t) F npu t1 < t < +, f(p,t) F npu - < t 0. u(p1) = M и u(t) u(f(p,t)) > M u(t) u(f(p,t)) t 0 npu t1 < t < +, u(t) > M t p1 f(p,t1).
u(t) p F - t 0. c t - c M f(p,t) F npu - < t 0, t1 0, f(p,t) f(p,t)F npu t1 t 0, D-(p) =, f(p,t) F npu - < t < t1, f(p,t) D-(p) f(p,t) u(p1) = m и u(t) u(f(p,t)) < m npu -< t < t1, p1 f(p,t1) u(t) M npu t -, p G D-(p) Цq K : u(q) = M, u(p) > M 1 D-(p) cвязнoe мнoжecmвo, p G u(p) < m (f(p,t),D-(p)) 0 npu t -. 1 T D-(p) t > 0 f(p,t) F f(p,t) 1 s T t s p F u(p) < m T T = (t1, +) t = t1 > 0 f(p,t) t1 = infT F f(p,t) F t1 < t < + t1 < t < + f(p,t)E t1 < t < + p1 f(p,t1)E p1 F u(p1) M f(p,t) F npu 0 t < + f(p,t) F t1 < t < + u(t) u(f(p,t)) u(t) > M t 0 u(t) < m u(t) < m t u(t1) = M u(t) c t + c m M = u(p1) = u(t1) < u(t) пpи t1 < t < + f(p,t) f(p,t) D+(p) 1 f(p,t) 1 u(t) m npu t +, ecли p F, тo f(p,t) F пpи - < t 0.
D+(p) Цq K : u(q) = m, p F D+(p) cвязнoe мнoжecmвo f(p,t)F пpи 0 t < +.
(f(p,t),D+(p)) 0 npu t +. F0 = F Fk = f(F, -k), k = 1,2,Е.
D+(p) F0 F1 Е Fk Е.
f(p,t) F 1 F F0 F1 Е Fk Е.
f(p,t) - < t p F p Fk k f(p,t) F 0 t k k f(p,t)F f(p,t) 0 t < + p F D-(p).
f(p,t)E - < t 0 D-(p) E E 1 D-(p) E = D-(p) E У E = F 1 E G D-(p) G F F D-(p) E G F = (K E) Цp G : u(p) = M; q D-(p) tk D-(p) G УG = K f(p,tk) q F = (K E) Цp G : u(p) = m; uq) = lim u(f(p,tk)) = lim utk) M ( ( k+ k+ q K m u(q) M u(q) M u(q) = M q D-(p) F = (K E) Цp G : u(p) = M Цp G : u(p) = m.
c = M 1 D-(p) F p F p F E p F p E p G p G E G E G p G f(p,t) p G УG = K F t p K p E f(p,t)F пpи - < t < +. p K E p p F p E p G p F E = F p F u(p) M 1 p p E u(p) M p F 1 p G u(p) = M p 1 u(p) M p K E p 1 p p K E p K p E K K 1 K p K E F E = F K F 1 1 p p F p 1 p G u(p) = M p F p E. G > 0 f(p,t)G | t |<. 1 1 u(t) u(f(p,t)) - < t < u(0) = u(f(p,0)) = u(p) = M < u(t) 0 < t < 1 f(p,t) E 0 < t < p = f(p,0) = lim f(p,t)E 1 0