A Multidimensional Singular Boundary Value Problem of the Cauchy-Nicoletti Type

Georgian Mathematical Journal

Volumn 4, Issue 4, 1997, Pages 303-312

  Diblik J ^a  

^a BRNO UNIVERSITY OF TECHNOLOGY   (Czech Republic)

Author keywords

Nonlinear Cauchy Nicoletti problem; Singular boundary value problem; Topological principle

Indexed keywords

EID: 0004607939     PISSN: 1072947X     EISSN: 15729176     Source Type: Journal    
DOI: 10.1515/GMJ.1997.303     Document Type: Article

References (19)

1. P. Hartman, Ordinary differential equations. Wiley, New York, London, Sydney, 1964.
2. L. K. Jackson and G. Klaassen, A variation of the topological method of Wazewski. SIAM J. Appl. Math. 20(1971), 124-130.
3. I. T. Kiguradze, On the Cauchy problem for singular systems of ordinary differential equations. (Russian) Differen tsial'nye Uravnenyia 1(1965), No. 10, 1271-1291.
4. I. T. Kiguradze, On the non-negative nonincreasing solutions of nonlinear second order differential equations. Ann. Mat. Pura Appl. 81(1969), 169-192.
5. I. T. Kiguradze, On a singular multi-point boundary value problem. Ann. Mat. Pura Appl. 86(1970), 367-400.
6. I. T. Kiguradze, Some singular boundary value problems for ordinary differential equations. (Russian) Tbilisi Univ. Press, Tbilisi, 1975.
7. Ju. A. Klokov and N. I. Vasiljev, The foundation of the theory of boundary value problems for ordinary differential equations. (Russian) Zi-natne, Riga, 1978.
8. N. B. Konyukhova, Singular Cauchy problems for systems of ordinary differential equations. (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 23(1983), No. 3, 629-645
9. English translation: Cornput. Math. Math. Phys. 23(1983), 72-82.
10. O. Nicoletti, Sulle condizioni Iniziali che determiniano gli integrale della equazioni differenziali ordinarie. Attt R. Acc. Sc. Torino 33(1897-1898), 746-759.
11. V. A. Chechyk, Investigation of systems of ordinary differential equations with singularity. (Russian) Proc. Moscov. Mat. Obshch. 8(1959), 155-198.
12. J. Diblík, On existence of O-curves of a singular system of differential equations. (Russian) Math. Nachr. 122(1985), 247-258.
13. J.Diblík, The singular Cauchy-Nicoletti problem for a system of two ordinary differential equations. Math. Bohem. 117(1992), 55-67.
14. Z. Šmarda, The existence and asymptotic behaviour of solutions of a certain class of the integrodifferential equations. Arch. Math. (Brno) 26(1990), 7-18.
15. B. Vrdoljak, On solutions of the general Lagerstrom equation. Z. Angew. Math. Mech. 67(1987), No. 5, T456-T458.
16. B. Vrdoljak, The increasing radial solutions of semilinear elliptic equations. 7th Czechoslovak Conference on Differential Equations and Their Applications, Extended abstracts, Partial differential equations, Numerical methods and applications, 107-109, Praha, Matematicky Ustav CSAV, 1989.
17. T. Werner, Singular Cauchy-Nicoletti problem with poles. Georgian Math. J. 2(1995), No. 2, 211-224.
18. T. WażCewski, Sur un principle topologique de l'examen de Failure asymptotique des intégrales des équations différentielles. Ann. Soc. Polon. Math. 20(1947), 279-313.
19. K. Borsuk, Theory of retracts. PWN (Polish Scientific Publishers), Warszawa, 1967.