Geodesic
The singular Cauchy-Nicoletti problem for the system of two ordinary differential equations
Mathematica Bohemica, Tome 117 (1992) no. 1, pp. 55-67

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
In the paper the singular Cauchy-Nicoletti problem for the system ot two ordinary differential equations is considered. New sufficient conditions for solvability of this problem are proved. In the proofs the topological method is applied. Some comparisons with known results are also given in the paper.
In the paper the singular Cauchy-Nicoletti problem for the system ot two ordinary differential equations is considered. New sufficient conditions for solvability of this problem are proved. In the proofs the topological method is applied. Some comparisons with known results are also given in the paper.
DOI : 10.21136/MB.1992.126234
Classification : 34B15, 54H25
Keywords: retract; singular Cauchy-Nicoletti problem 
Diblík, Josef. The singular Cauchy-Nicoletti problem for the system of two ordinary differential equations. Mathematica Bohemica, Tome 117 (1992) no. 1, pp. 55-67. doi: 10.21136/MB.1992.126234
@article{10_21136_MB_1992_126234,
     author = {Dibl{\'\i}k, Josef},
     title = {The singular {Cauchy-Nicoletti} problem for the system of two ordinary differential equations},
     journal = {Mathematica Bohemica},
     pages = {55--67},
     year = {1992},
     volume = {117},
     number = {1},
     doi = {10.21136/MB.1992.126234},
     mrnumber = {1154055},
     zbl = {0817.34013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1992.126234/}
}
TY  - JOUR
AU  - Diblík, Josef
TI  - The singular Cauchy-Nicoletti problem for the system of two ordinary differential equations
JO  - Mathematica Bohemica
PY  - 1992
SP  - 55
EP  - 67
VL  - 117
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1992.126234/
DO  - 10.21136/MB.1992.126234
LA  - en
ID  - 10_21136_MB_1992_126234
ER  - 
%0 Journal Article
%A Diblík, Josef
%T The singular Cauchy-Nicoletti problem for the system of two ordinary differential equations
%J Mathematica Bohemica
%D 1992
%P 55-67
%V 117
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1992.126234/
%R 10.21136/MB.1992.126234
%G en
%F 10_21136_MB_1992_126234

[1] M.S. Baouendi, C. Goulaouic: Singular nonlinear Cauchy problems. J. Differential equations 22 (1976), 268-291. | DOI | MR | Zbl

[2] K. Borsuk: Theory of retracts. PWN, Warszawa, 1967. | MR | Zbl

[3] V. A. Chechyk: Investigation of systems of ordinary differential equations with singularity. Proc. Moscow math. soc. 8 (1959), 155-198. (In Russian.) | MR

[4] J. Diblík: On existence of $\delta$-bounded solutions of a nonhomogeneous linear system of differential equations. Funkcialaj Ekvacioj 34 no. 1 (1991), 1-18. | MR

[5] P. Hartman: Ordinary differential equations. Wiley, 1964. | MR | Zbl

[6] L. Jackson, G. Klaassen: A variation of the topological method of Ważewski. SIAM J. Appl. Math. 20 (1971), 124-130. | DOI | MR

[7] I. T. Kiguradze: Some singular boundary value problems for ordinary differential equations. Tbilisi Univ. Press, Tbilisi, 1975. (In Russian.) | MR

[8] Ju. A. Klokov, N. I. Vasiljev: The foundations of the theory of boundary value problems for ordinary differential equations. Zinatne, Riga, 1978. (In Russian.)

[9] N. B. Konyukhova: Singular Cauchy problems for systems of ordinary differential equations. U.S.S.R. Comput. Math. and Math. Phys. 23 (1983), 72-82. | DOI | MR | Zbl

[10] A. Lasota, C. Olech: An optimal solution of Nicoletti's boundary value problem. Ann. Polon. Math. 18 no. 2 (1966), 131-139. | DOI | MR | Zbl

[11] A. Lasota: Sur l' existence et l'unicité des solutions du probléme aux limites de Nicoletti pour un systéme d'equations différentielles ordinaires. Zeszyty Nauk, UJ, Prace Mat. 11 (1966), 41-48. | MR | Zbl

[12] S. K. Norkin: Asymptotic behavior of solutions of a multidimensional system. Differential equations 21 (1985), 654-657. | MR

[13] P. K. Palamides: A topological method and its application on a general boundary value problem. Nonlinear Analysis, Theory and Applications 7(1983), 1101-1114. | MR | Zbl

[14] B. Půža: On one class of solvable boundary value problems for a system of ordinary differential equations. 7th Czechoslovak Conference on Differential Equations and Their Applications, Enlarged abstracts, Ordinary differential equations, Praha, 1989, pp. 76-78.

[15] A. N. Vityuk: The generalized Cauchy problem for the system of differential equations not solved with respect to derivatives. Differencialnyje uravněnija 7 (1971), 1575-1580. (In Russian.) | MR

[16] B. Vrdoljak: On solutions of the Lagerstrom equation. Archivum Mathematicum 24 (1988), 111-122, Brno. | MR | Zbl

[17] B. Vrdoljak: The increasing negative radial solutions of semilinear elliptic equations. 7th Czechoslovak Conference on Differential Equations and Their Applications, Enlarged abstracts, Partial differential equations, Numerical methods and applications, Praha, 1989, pp. 107-109.

[18] T. Ważewski: Sur un principe topologique de l'examen de l'allure asymptotique des intégrales des équations différentielles. Ann. Soc. Polon. Math. 20 (1947), 279-313. | MR

Cité par Sources :