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ON SOME PROBLEMS OF BEHAVIOUR OF SOLUTIONS OF THE DIFFERENTIAL EQUATIONS IN HILBERT SPACE

ON SOME PROBLEMS OF BEHAVIOUR OF SOLUTIONS OF THE DIFFERENTIAL EQUATIONS IN HILBERT SPACE DEMONSTRATIO MATHEMATICAT o i . IIINo 41971Hpeia Myom, EXH MyraHHCKH0 HEKOTOPHX BOHPOCAX nOBE^EHHfl PEEOLEHHÖ .KMiEPEBUHAJIBHHX yPABHEHHÉB IIPOCTPAHCTBE TMLEEPTA(Irena Musial, Jerzy MuszynskiON SOME PROBLEMS OF BEHAVIOUR OF SOLUTIONSOF THE DIFFERENTIAL EQUATIONS IN HILBERT SPACE)1 . B paöOTax [ 6 ] , [ 7 ] paccMaTpuBajiHctqecKoro noBefleHUHpaBHeHHäsonpocu acHMnTOTH-HeKOTOpnx oÓHKHOBeHHux flH$(fepeHD,HajibHHX y -ranax + <xx + ßx = 0,x( 0) = x±x(0) = x Q ,(1)h qacTHHX AH$$epeHitHajii.HHX ypaBHeHHM THnaa t t + a u t + ßu = a g g ,u(s,0) = f Q ( s ) ,npn HeKOTopnx oflHopoflHHXITOOCfßHBJiaiOTCHu t ( s , 0 ) = f 1 (s)rpaHHtiHhix ycjiOBHüx.HeKOTOpHMHb < ß < B.üpeflnojiarajiocB(fyHKAHHMH - HJIH OnepaTOpaMH CopraHiraeHHHMH oßjiacTHMH 3HaieHHÄ qepe30 < a < a 4 A,(2)HeKOTopne nocTOHHHHe:0ica3aJiocB qTO cymecTByeT6ojibmoecxoflOTBO nojiy^eHHUX pe3yjitTaTOB. 3TO He cjijniagHO - e r oMOXHanojiyiHTb npH öojiee aöcTpaKTHOÜ nocTaHOBKe 3afla^i THna ( 1 )( 2 ) - noJiyqeHHHe B ynOMHHyTHX paöoTax pe3yjiBTamHJIHMoraa nojiy-qHTB H npn öojiee oßmeM noflxofle,oxBaTHBarnHM flonojiHHTejitHO HeKOTOpue He paccMOTpeHHHe qacTHHe 3 a f l a r a .B CTaTte o6o6maKTCfllaio KorflaTOJIBKOiaCTH paßoT, OTHOcnmHecJiß HB^aeTCH (fyHKiiHeftß = &(x) - ßTOJIBKOKoflHoro nepeMeHHOrocjiyx,ciaiiHOHapHa. ÄajiBHeämHe oßoÖmeHHH 6y,nyT onyßjiH-KOBaHH ii03ace.2. IlyCTbCTpaHCTBOM,1 — H,I.HHBJIHeTCHI = <0, » ) .onpeaeJieHHHX H kÄeÖCTBHTeJIBHUMTHJIBSepTOBHMIlyCTBKjiaccCk(I)-fyHKIiHiinpox:pa3 HenpepnBHO flH$$epeHHHpyeMHX HaHx 3Ha^eHHa 6y,neM o6o3HaiaT£ ^epe3PaccMOTpHM http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON SOME PROBLEMS OF BEHAVIOUR OF SOLUTIONS OF THE DIFFERENTIAL EQUATIONS IN HILBERT SPACE

Musial, Irena; Muszynski, Jerzy
Demonstratio Mathematica , Volume 3 (4): 20 – Oct 1, 1971
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Publisher
de Gruyter
Copyright
© by Irena Musial
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1971-0404
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAT o i . IIINo 41971Hpeia Myom, EXH MyraHHCKH0 HEKOTOPHX BOHPOCAX nOBE^EHHfl PEEOLEHHÖ .KMiEPEBUHAJIBHHX yPABHEHHÉB IIPOCTPAHCTBE TMLEEPTA(Irena Musial, Jerzy MuszynskiON SOME PROBLEMS OF BEHAVIOUR OF SOLUTIONSOF THE DIFFERENTIAL EQUATIONS IN HILBERT SPACE)1 . B paöOTax [ 6 ] , [ 7 ] paccMaTpuBajiHctqecKoro noBefleHUHpaBHeHHäsonpocu acHMnTOTH-HeKOTOpnx oÓHKHOBeHHux flH$(fepeHD,HajibHHX y -ranax + <xx + ßx = 0,x( 0) = x±x(0) = x Q ,(1)h qacTHHX AH$$epeHitHajii.HHX ypaBHeHHM THnaa t t + a u t + ßu = a g g ,u(s,0) = f Q ( s ) ,npn HeKOTopnx oflHopoflHHXITOOCfßHBJiaiOTCHu t ( s , 0 ) = f 1 (s)rpaHHtiHhix ycjiOBHüx.HeKOTOpHMHb < ß < B.üpeflnojiarajiocB(fyHKAHHMH - HJIH OnepaTOpaMH CopraHiraeHHHMH oßjiacTHMH 3HaieHHÄ qepe30 < a < a 4 A,(2)HeKOTopne nocTOHHHHe:0ica3aJiocB qTO cymecTByeT6ojibmoecxoflOTBO nojiy^eHHUX pe3yjitTaTOB. 3TO He cjijniagHO - e r oMOXHanojiyiHTb npH öojiee aöcTpaKTHOÜ nocTaHOBKe 3afla^i THna ( 1 )( 2 ) - noJiyqeHHHe B ynOMHHyTHX paöoTax pe3yjiBTamHJIHMoraa nojiy-qHTB H npn öojiee oßmeM noflxofle,oxBaTHBarnHM flonojiHHTejitHO HeKOTOpue He paccMOTpeHHHe qacTHHe 3 a f l a r a .B CTaTte o6o6maKTCfllaio KorflaTOJIBKOiaCTH paßoT, OTHOcnmHecJiß HB^aeTCH (fyHKiiHeftß = &(x) - ßTOJIBKOKoflHoro nepeMeHHOrocjiyx,ciaiiHOHapHa. ÄajiBHeämHe oßoÖmeHHH 6y,nyT onyßjiH-KOBaHH ii03ace.2. IlyCTbCTpaHCTBOM,1 — H,I.HHBJIHeTCHI = <0, » ) .onpeaeJieHHHX H kÄeÖCTBHTeJIBHUMTHJIBSepTOBHMIlyCTBKjiaccCk(I)-fyHKIiHiinpox:pa3 HenpepnBHO flH$$epeHHHpyeMHX HaHx 3Ha^eHHa 6y,neM o6o3HaiaT£ ^epe3PaccMOTpHM

Journal

Demonstratio Mathematica – de Gruyter

Published: Oct 1, 1971

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