Download e-book for kindle: Introduction to classical real analysis by Karl Stromberg

J(s)ids. 5) has at least one solution. 1. Since pW' + p'W = 0, p(s)W(s) = constant, and so suptE[o, 1] lp(t)Gt(t, s)l ~ Dop(s) for some constant Do. Proof.

3 lim p(t)u'(t) = au(1) + b lim p(t)u'(t) Consequently u independent. = 0, 0. 3 lim p(t)y~(t), Q4 = ay1(1) + b lim p(t)y~(t) t-tO+ t-+O+ t-+1- t-+1- and Q5 = Q { 1 [y1(s)y2(1) a 1 ( ) ( ) '( ))d Y1(1)y2(s)]f( s,y s , p s y s s W(s) lo { 1 [Y1 (s) t~lf- p(t)y~(t) -y2 (s) t~lf- p(t)y~ (t)] W(s) +bQ1j0 f(s, y(s),p(s)y'(s))ds. Note that Q3Q2 - Q4Q1 =1- 0. To see this let u(x) = Q1y1(x) - Q3y2(x). e. on [0, 1] and - au(O) + {3x limt-to+ p(t)u'(t) = 0. If Q3Q2-Q4Q1 = 0 then au(l)+blimt-t 1- p(t)u'(t) = 0.

Download PDF sample

Introduction to classical real analysis by Karl Stromberg


by John
4.0

Rated 4.41 of 5 – based on 24 votes