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89 sonuçtan 1-3 arası sonuçlar
Sayfa 4
Fact 2 ( Nondegeneracy ) . If u € P + ( M ) , then for all 20 = ( xo , to ) e D ( u ) we
have sup u > u ( ro , t Qe ( 20 ) p > 0 . 2n + 1 Proof . The proof of this statement is
similar to that of ( Ca2 , Lemma 1 ) . Without loss of generality , we assume that zo
...
Fact 2 ( Nondegeneracy ) . If u € P + ( M ) , then for all 20 = ( xo , to ) e D ( u ) we
have sup u > u ( ro , t Qe ( 20 ) p > 0 . 2n + 1 Proof . The proof of this statement is
similar to that of ( Ca2 , Lemma 1 ) . Without loss of generality , we assume that zo
...
Sayfa 5
By Fact 1 , it suffices to check that D ; D ; Um ( 2 ) ▻ D ; D ; Um ( z ) , OkUm ( 2 ) ▻
OU ( z ) for a . e . z ER * + 1 . If z = ( x , t ) E N ( umo ) , then for some p > 0 and
sufficiently large m in the p neighborhood of z we have H [ Um – Ux ] = 0 . By the
...
By Fact 1 , it suffices to check that D ; D ; Um ( 2 ) ▻ D ; D ; Um ( z ) , OkUm ( 2 ) ▻
OU ( z ) for a . e . z ER * + 1 . If z = ( x , t ) E N ( umo ) , then for some p > 0 and
sufficiently large m in the p neighborhood of z we have H [ Um – Ux ] = 0 . By the
...
Sayfa 132
39b ) a ( 2 ) ( n ) = e - iol O ( 1 - 1 ( an + Cn + 1 - 1 ) ) ) L O ( 1 - 192 ) The fact that
the solutions â ( 1 ) ( n ) and â ( 2 ) ( n ) are linearly independent follows from ( 1 .
1 . 39 ) . Thus , we have proved the last statement of the theorem . We recall that ...
39b ) a ( 2 ) ( n ) = e - iol O ( 1 - 1 ( an + Cn + 1 - 1 ) ) ) L O ( 1 - 192 ) The fact that
the solutions â ( 1 ) ( n ) and â ( 2 ) ( n ) are linearly independent follows from ( 1 .
1 . 39 ) . Thus , we have proved the last statement of the theorem . We recall that ...
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algebraic analytic apply assume basis boundary bounded called chain homotopy closed coefficients complex computation condition connection Consequently consider constant construction contains continuous convex corresponding defined definition deformation denote determined differential domain element equal equation equivalence estimate example exists extension fact field finite fixed formula function given identity implies inequality integral intersection introduce invariant inverse isomorphism Lemma linear Math Mathematical matrix measure metric Moreover natural normal Observe obtain Obviously operator orientation particular periodic positive present problem projective Proof properties Proposition prove regular relation Remark respectively result ring satisfies scheme sequence singular smooth solutions space standard statement Subsection suffices Suppose takes Theorem theory transformation true twists unique vector weight zero