Previous |  Up |  Next

Article

Keywords:
generalized Riccati differential equation; global solutions
Summary:
We present an integral comparison theorem which guarantees the global existence of a solution of the generalized Riccati equation on the given interval $[a,b)$ when it is known that certain majorant Riccati equation has a global solution on $[a,b)$.
References:
[1] Došlý, O., Řehák, P.: Half-linear differential equations. North-Holland, Elsevier, Amsterdam, 2005. MR 2158903 | Zbl 1090.34001
[2] Erbe, L.: Integral comparison theorems for scalar Riccati equations and applications. Canad. Math. Bull. 25 (1982), 82–97. DOI 10.4153/CMB-1982-012-8 | MR 0657656
[3] Hasil, P.: Conditional oscillation of half-linear differential equations with periodic coefficients. Arch. Math. (Brno) 44 (2008), 119–131. MR 2432849
[4] Hasil, P., Veselý, M.: Oscillation and non-oscillation of half-linear differential equations with coefficients having mean values. Open Math. 16 (1) (2018), 507–521. DOI 10.1515/math-2018-0047 | MR 3800645
[5] Jaroš, J., Kusano, T., Tanigawa, T.: Nonoscillatory solutions of planar half-linear differential systems: a Riccati equation approach. EJQTDE 92 (2018), 1–28. MR 3884523
[6] Mirzov, J.D.: Asymptotic Properties of Solutions of Systems of Nonlinear Nonautonomous Ordinary Differential Equations. Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math. 14 (2004), 175 pp. MR 2144761 | Zbl 1154.34300
[7] Stafford, R.A., Heidel, J.W.: A new comparison theorem for scalar Riccati equations. Bull. Amer. Math. Soc. 80 (1974), 754–757. DOI 10.1090/S0002-9904-1974-13588-3 | MR 0342771
[8] Travis, C.C.: Remarks on a comparison theorem for scalar Riccati equations. Proc. Amer. Math. Soc. 52 (1975), 311–314. DOI 10.1090/S0002-9939-1975-0377188-X | MR 0377188
Partner of
EuDML logo