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GREEN'S FUNCTIONS AND BOUNDARY VALUE PROBLEMS FOR SOME CLASS OF ORDINARY DIFFERENTIAL EQUATIONS

GREEN'S FUNCTIONS AND BOUNDARY VALUE PROBLEMS FOR SOME CLASS OF ORDINARY DIFFERENTIAL EQUATIONS DEMONSTRATIO MATHEMATICAVol. XVIIINo 31985Feliks Baranski, Jan MusialekGREEN'S FUNCTIONS AND BOUNDARY VALUE PROBLEMSFOR SOME CLASS OF ORDINARY DIFFERENTIAL EQUATIONS1. IntroductionIn the present paper we shall oonsider the problems ofuniqueness and existence of the solutions of the boundaryvalue problems for the equationst(1)Lu(x) « f ( x ) ,(1a)Lu(x) = f ( x , u ( x ) ) ,(2)L 2 u(x) = f ( x ) ,(2a)L 2 u(x) - f ( x , u ( x ) ) tfor xe J = ( a , b ) , a < b , a,b being o one tant 8, wherepo3 (D - q ( x ) ) u , L u « LLu, and boundary data:(3)u(a) = A.j,u(b) - B v(4)D x u(a) = A 2 ,Dxu(b) «= B 2 ,(5)(Dx+h.,)u(a) « k y(D x +h 2 )u(b) = B(6)u(a) « A^,(Dx+h)u(b) = B 4Lu =for the equations ( 1 ) , (1a) and boundary datai(3a)D^u(a) = C i tDxu(b) = D i fi.The results of this paper were presented during the 3rdSymposium on Integral Equations and Their Applications heldat the Technical University of Warsaw, December 3-6, 1984.- 743 -?» BaraAskl. J ,*t4a)MusiaiekD*u(a) » C±,D*u(b) = D ± ,i-1,3,(5a)bJ(D -tf^Juia) = http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

GREEN'S FUNCTIONS AND BOUNDARY VALUE PROBLEMS FOR SOME CLASS OF ORDINARY DIFFERENTIAL EQUATIONS

Baranski, Feliks; Musialek, Jan
Demonstratio Mathematica , Volume 18 (3): 20 – Jul 1, 1985
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Publisher
de Gruyter
Copyright
© by Feliks Baranski
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1985-0308
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XVIIINo 31985Feliks Baranski, Jan MusialekGREEN'S FUNCTIONS AND BOUNDARY VALUE PROBLEMSFOR SOME CLASS OF ORDINARY DIFFERENTIAL EQUATIONS1. IntroductionIn the present paper we shall oonsider the problems ofuniqueness and existence of the solutions of the boundaryvalue problems for the equationst(1)Lu(x) « f ( x ) ,(1a)Lu(x) = f ( x , u ( x ) ) ,(2)L 2 u(x) = f ( x ) ,(2a)L 2 u(x) - f ( x , u ( x ) ) tfor xe J = ( a , b ) , a < b , a,b being o one tant 8, wherepo3 (D - q ( x ) ) u , L u « LLu, and boundary data:(3)u(a) = A.j,u(b) - B v(4)D x u(a) = A 2 ,Dxu(b) «= B 2 ,(5)(Dx+h.,)u(a) « k y(D x +h 2 )u(b) = B(6)u(a) « A^,(Dx+h)u(b) = B 4Lu =for the equations ( 1 ) , (1a) and boundary datai(3a)D^u(a) = C i tDxu(b) = D i fi.The results of this paper were presented during the 3rdSymposium on Integral Equations and Their Applications heldat the Technical University of Warsaw, December 3-6, 1984.- 743 -?» BaraAskl. J ,*t4a)MusiaiekD*u(a) » C±,D*u(b) = D ± ,i-1,3,(5a)bJ(D -tf^Juia) =

Journal

Demonstratio Mathematica – de Gruyter

Published: Jul 1, 1985

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