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Ergebnisse 1-3 von 27
Seite 291
The proof of lim u r = 0 is similar to the above lemma . We also need the following lemma in the sense of backward . 2 < = no LEMMA 2.4 . If u is a solution of ( 1.1 ) and if ( a ) u , 20 , ( 2.6 ) ( b ) Δυ , -1 So , for some n = N > 2 ...
The proof of lim u r = 0 is similar to the above lemma . We also need the following lemma in the sense of backward . 2 < = no LEMMA 2.4 . If u is a solution of ( 1.1 ) and if ( a ) u , 20 , ( 2.6 ) ( b ) Δυ , -1 So , for some n = N > 2 ...
Seite 294
PROOF . Suppose un - , < 0 , then u has no other generalized zeros . Lemma 2.6 implies ( 1 ) . Since un > 0 , A UN > 0 , Lemma 2.2 implies u , 20 , Au , 20 , for all nN and ( 3.1 ) u . > 0 for all nN + 2 . and Au , > 0 for all n N +1 .
PROOF . Suppose un - , < 0 , then u has no other generalized zeros . Lemma 2.6 implies ( 1 ) . Since un > 0 , A UN > 0 , Lemma 2.2 implies u , 20 , Au , 20 , for all nN and ( 3.1 ) u . > 0 for all nN + 2 . and Au , > 0 for all n N +1 .
Seite 341
where the last equality follows from Lemma 3.1 and condition B. Combining ( 3.31 ) . ( 3.31 ) , ( 3.36 ) . ( 3.37 ) we have 2 9 ) ( 3.38 ) 11301 : on a.s. as n + 8 Finally , it is easy to see that ( 3.39 ) 4n + n 1 lian !
where the last equality follows from Lemma 3.1 and condition B. Combining ( 3.31 ) . ( 3.31 ) , ( 3.36 ) . ( 3.37 ) we have 2 9 ) ( 3.38 ) 11301 : on a.s. as n + 8 Finally , it is easy to see that ( 3.39 ) 4n + n 1 lian !
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