The Solution of Some Turning Point Problems

Cover The Solution of Some Turning Point Problems
The Solution of Some Turning Point Problems
Herbert Kurss
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For t large (i].. 13) has a solution T whose last two columns are asymptotic to a constant multiplied by the last two columns of E. Select i^ in (i|. 10) so that this T is the solution to (1;. 13) which corresponds to (I4.. IO). Let [QE' ] denote the last two columns of GE' . Then in A :&:■ 38 {i4.. L5a) [GE"-'-] < const i 1 t"*- t < o ~ ik'lSh) [GE"-^] < const, ltl < t where t is a fixed, but sufficiently large, real number. The first global estimate for GE~ which follows from (i|. L5) is (i4.. L6) [GE'-*-] < const 1 1 ^ 1 t^ 1 1 1 -1 1 1 all t in i. E. , from (i;. 8) and ([|.. 9) (l|. 17) [GE"-'-] < const 3 1 1 x5. 1 1 1 1 -1 1 1 , all t in J The second global estimate which follows from (Li-. LS) is (i+. L8) [GE'-'-] < const 1 t 1 -1 1 all t in y^ i. E. , from (l+. S) and (li.. 9) 39 (14.. 19) [GE"-'-] < const 1 2 1 Z ] p' 1 1 IT 'Z t + p J , all t in // In order to carry over these results to H of (i^-. Ij. ) define E = where E is defined by (I4.. IL1. ), and define 1 ■ E (1;.

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