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Asymptotic Equivalence of Differential Equation in Banach Space

Asymptotic Equivalence of Differential Equation in Banach Space DEMONSTRATIO MATHEMATICAVoL x x nNo 21989Jaroslaw M o r c h a l oASYMPTOTIC EQUIVALENCE OF DIFFERENTIAL EQUATIONIN BANACH SPACE1 . The purpose of t h i s paper i s the study of thet i c e q u i v a l e n c e between the s o l u t i o n s of theasympto-differentialeq u a t i o n s(I)x'= A(t)x + f ( t , x , T ( x ) )and(II)x= A(t)xi n Banach space B. Here x , f are the e l e m e n t s of E, A ( t )isa l i n e a r o p e r a t o r on E<> More p r e c i s e l y , we g i v e some c o n d i t i o n s which guarantee t h a t f o r each bounded s o l u t i o n y : J — - B(J = < 0 , ) ,E-Banaoh space w i t h norm ||*||) of ( I I )theree x i s t s a bounded http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

Asymptotic Equivalence of Differential Equation in Banach Space

Morchalo, Jaroslaw
Demonstratio Mathematica , Volume 22 (2): 12 – Apr 1, 1989
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Publisher
de Gruyter
Copyright
© by Jaroslaw Morchalo
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1989-0206
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVoL x x nNo 21989Jaroslaw M o r c h a l oASYMPTOTIC EQUIVALENCE OF DIFFERENTIAL EQUATIONIN BANACH SPACE1 . The purpose of t h i s paper i s the study of thet i c e q u i v a l e n c e between the s o l u t i o n s of theasympto-differentialeq u a t i o n s(I)x'= A(t)x + f ( t , x , T ( x ) )and(II)x= A(t)xi n Banach space B. Here x , f are the e l e m e n t s of E, A ( t )isa l i n e a r o p e r a t o r on E<> More p r e c i s e l y , we g i v e some c o n d i t i o n s which guarantee t h a t f o r each bounded s o l u t i o n y : J — - B(J = < 0 , ) ,E-Banaoh space w i t h norm ||*||) of ( I I )theree x i s t s a bounded

Journal

Demonstratio Mathematica – de Gruyter

Published: Apr 1, 1989

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