Previous |  Up |  Next


retract; singular Cauchy-Nicoletti problem
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.
[1] M.S. Baouendi, C. Goulaouic: Singular nonlinear Cauchy problems. J. Differential equations 22 (1976), 268-291. DOI 10.1016/0022-0396(76)90028-0 | MR 0435564 | Zbl 0344.35012
[2] K. Borsuk: Theory of retracts. PWN, Warszawa, 1967. MR 0216473 | Zbl 0153.52905
[3] V. A. Chechyk: Investigation of systems of ordinary differential equations with singularity. Proc. Moscow math. soc. 8 (1959), 155-198. (In Russian.) MR 0107066
[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 1116878
[5] P. Hartman: Ordinary differential equations. Wiley, 1964. MR 0171038 | Zbl 0125.32102
[6] L. Jackson, G. Klaassen: A variation of the topological method of Ważewski. SIAM J. Appl. Math. 20 (1971), 124-130. DOI 10.1137/0120016 | MR 0279377
[7] I. T. Kiguradze: Some singular boundary value problems for ordinary differential equations. Tbilisi Univ. Press, Tbilisi, 1975. (In Russian.) MR 0499402
[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 10.1016/S0041-5553(83)80104-9 | MR 0706888 | Zbl 0555.34002
[10] A. Lasota, C. Olech: An optimal solution of Nicoletti's boundary value problem. Ann. Polon. Math. 18 no. 2 (1966), 131-139. DOI 10.4064/ap-18-2-131-139 | MR 0204742 | Zbl 0144.10301
[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 0281986 | Zbl 0286.34025
[12] S. K. Norkin: Asymptotic behavior of solutions of a multidimensional system. Differential equations 21 (1985), 654-657. MR 0801454
[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 0719362 | Zbl 0525.34017
[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 0289833
[16] B. Vrdoljak: On solutions of the Lagerstrom equation. Archivum Mathematicum 24 (1988), 111-122, Brno. MR 0983229 | Zbl 0674.34024
[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 0026206
Partner of
EuDML logo