Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

ON EXISTENCE OF SOLUTIONS OF A SINGULAR CAUCHY-NICOLETTI PROBLEM FOR A SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONS

ON EXISTENCE OF SOLUTIONS OF A SINGULAR CAUCHY-NICOLETTI PROBLEM FOR A SYSTEM OF... D E M O N S T R A T E MATHEMATICAVol. XXXNo 41997Jaromir Bastinec, Josef DiblikON EXISTENCE OF SOLUTIONSOF A SINGULAR CAUCHY-NICOLETTI PROBLEMFOR A SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONSA b s t r a c t . In the paper a singular problem of the type of Cauchy-Nicoletti for asystem of integro-differential equations is considered. The existence of solutions the graphof which remains in a properly choosen domain is proved. Moreover, the theorem aboutuniqueness of solution in this domain is given. The applicability of results is showed onan illustrative example.1. IntroductionConsider the following singular problem of the type of Cauchy-Nicolettifor the system of n ordinary integro-differential equationsXy'k(x)=fk(x,y(x))+\gk(x,s,y(x),y(s))ds,aby'i(x)= Mx,y(x))+J gi(x,s,y(x),y(s))ds,xk = 1,2,..(2).,h,+Vk(a )1 < h < n, I = h + 1,..= Ak,yi(b~)=.,n,Bi,where x € I = (a,b), y(x) = (y1(x),y2(x),..,,yn(x)),a,b,Ak,B,are realconstants, a < b and (x,y) G I x D, where the set D C R n is indicatedbelow.The Cauchy-Nicoletti problem, the generalized Cauchy problems or theboundary value problems for systems of ordinary differential equations havebeen considered by many authors. Singular problems of such types havebeen studied e.g. in works [l]-[9], [11]. Singular initial problem for systemsKey words and phrases: singular problem of the type of Cauchy-Nicoletti, uniquenessof solutions, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON EXISTENCE OF SOLUTIONS OF A SINGULAR CAUCHY-NICOLETTI PROBLEM FOR A SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONS

Bastinec, Jaromír; Diblik, Josef
Demonstratio Mathematica , Volume 30 (4): 14 – Oct 1, 1997
Download PDF
14 pages

Loading next page...
 
/lp/de-gruyter/on-existence-of-solutions-of-a-singular-cauchy-nicoletti-problem-for-a-8C9aznG4Do

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
de Gruyter
Copyright
© by Jaromír Bastinec
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1997-0406
Publisher site
See Article on Publisher Site

Abstract

D E M O N S T R A T E MATHEMATICAVol. XXXNo 41997Jaromir Bastinec, Josef DiblikON EXISTENCE OF SOLUTIONSOF A SINGULAR CAUCHY-NICOLETTI PROBLEMFOR A SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONSA b s t r a c t . In the paper a singular problem of the type of Cauchy-Nicoletti for asystem of integro-differential equations is considered. The existence of solutions the graphof which remains in a properly choosen domain is proved. Moreover, the theorem aboutuniqueness of solution in this domain is given. The applicability of results is showed onan illustrative example.1. IntroductionConsider the following singular problem of the type of Cauchy-Nicolettifor the system of n ordinary integro-differential equationsXy'k(x)=fk(x,y(x))+\gk(x,s,y(x),y(s))ds,aby'i(x)= Mx,y(x))+J gi(x,s,y(x),y(s))ds,xk = 1,2,..(2).,h,+Vk(a )1 < h < n, I = h + 1,..= Ak,yi(b~)=.,n,Bi,where x € I = (a,b), y(x) = (y1(x),y2(x),..,,yn(x)),a,b,Ak,B,are realconstants, a < b and (x,y) G I x D, where the set D C R n is indicatedbelow.The Cauchy-Nicoletti problem, the generalized Cauchy problems or theboundary value problems for systems of ordinary differential equations havebeen considered by many authors. Singular problems of such types havebeen studied e.g. in works [l]-[9], [11]. Singular initial problem for systemsKey words and phrases: singular problem of the type of Cauchy-Nicoletti, uniquenessof solutions,

Journal

Demonstratio Mathematica – de Gruyter

Published: Oct 1, 1997

There are no references for this article.