On the Behavior of Solutions of Some Systems of Differential Equations Partially Solved with Respect to the Derivatives in the Presence of a Pole
- 19 Downloads
We study the existence of analytic solutions for some systems of ordinary differential equations partially solvable with respect to the derivatives. We establish sufficient conditions for the existence of analytic solutions of the Cauchy problem in the presence of a pole. An estimate for these solutions is obtained in a certain domain and the problem of the number of solutions is investigated.
Unable to display preview. Download preview PDF.
- 3.R. G. Grabovskaya and J. Diblic, Asymptotics of Systems of Differential Equations Unsolved with Respect to the Derivatives [in Russian], Dep. at VINITI, No. 1786.Google Scholar
- 5.G. E. Samkova, “Existence and asymptotic behavior of the analytic solutions of some singular differential systems unsolved with respect to the derivatives,” Differents. Uravn., 27, No. 11, 2012–2013 (1991).Google Scholar
- 6.G. E. Samkova and N. V. Sharai, “On the investigation of one semiexplicit system of differential equations in the case of a variable pencil of matrices,” Nelin. Kolyv., 5, No. 2, 224–236 (2002); English translation: Nonlin. Oscillat., 5, No. 2, 215–226 (2002).Google Scholar
- 7.A. M. Samoilenko, “On the asymptotic integration of a system of linear differential equations with a small parameter in the coefficients of a part of derivatives,” Ukr. Mat. Zh., 54, No. 11, 1505–1516 (2002); English translation: Ukr. Math. J., 54, No. 11, 1825–1841 (2002).Google Scholar
- 8.N. V. Sharai and H. E. Samkova, “Asymptotics of solutions of some semiexplicit systems of differential equations,” Nauk. Visn. Cherniv. Univ., Ser. Mat., Issue 314–315, 181–188 (2006).Google Scholar
- 10.J. Diblic, “On the asymptotic behavior of solutions of a certain system of quasilinear differential equations not solved with respect to derivatives,” Rici Mat. Univ. Parma, No. 13, 413–419 (1987).Google Scholar
- 12.J. Malmquist, “Sur l’edude analitique des solutions d’un systeme d’equations differentielles dans le voisinage d’un point singulier d’indetermination,” Acta Math., 1–64, 73, 74, 87–129, 109–128 (1941).Google Scholar
- 13.O Song Guk, Pak Ponk, and Chol Permissible, “Boundary condition of a system of linear ordinary differential equations in a closed angle domain of complex plane,” Kwahakwon Thongbo Bull. Acad. Sci. DPR Korea, No. 3, 2–4 (2001).Google Scholar
- 14.W. Strodt, “Contributions to the asymptotic theory of ordinary differential equations in the complex domain,” Mem. Amer. Math. Soc., No. 13, 1–81 (1957).Google Scholar
- 15.W. Trjitzinsky, “Theory of nonlinear singular differential system,” Trans. Amer. Math. Soc., No. 42, 225–321 (1937).Google Scholar
- 16.T. Wazewski, “Sur l’evaluation du domaine d’existence des fonctions implicites reelles ou complexes,” Ann. Soc. Pol. Math., No. 20, 81–120 (1947).Google Scholar