Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
Riemann–Weber half-linear differential equation; principal solution; modified Riccati equation; asymptotic formula
Riemann–Weber half-linear differential equation; principal solution; modified Riccati equation; asymptotic formula
Summary:
We establish an asymptotic formula for a pair of linearly independent solutions of the subcritical Riemann–Weber type half-linear differential equation. We also complement the results of the author and M. Ünal, Acta Math. Hungar. 120 (2008), 147–163, where the equation was considered in the critical case.
References:
[1] Agarwal, R.P., Grace, S.R., O’Regan, D.: Oscillation Theory of Second Order Linear, Half-Linear, Superlinear and Sublinear Differential Equations. Kluwer Acad. Publ., Dordrecht, Boston, London, 2002. MR 2091751
[2] Došlý, O., Elbert, Á.: Integral characterization of principal solution of half-linear differential equations. Studia Sci. Math. Hungar. 36 (2000), 455–469. MR 1798750
[3] Došlý, O., Fišnarová, S.: Half-linear oscillation criteria: Perturbation in term involving derivative. Nonlinear Anal. 73 (2010), 3756–3766. DOI 10.1016/j.na.2010.07.049 | MR 2728552 | Zbl 1207.34041
[4] Došlý, O., Řehák, P.: Half-Linear Differential Equations. vol. 202, North-Holland Mathematical Studies, Elsevier, Amsterdam, 2005. MR 2158903 | Zbl 1090.34001
[5] Došlý, O., Ünal, M.: Conditionally oscillatory half-linear differential equations. Acta Math. Hungar. 120 (2008), 147–163. DOI 10.1007/s10474-007-7120-4 | MR 2431365 | Zbl 1199.34169
[6] Došlý, O., Yamaoka, N.: Oscillation constants for second-order ordinary differential equations related to elliptic equations with $p$-Laplacian. Nonlinear Anal. 113 (2015), 115–136. MR 3281849 | Zbl 1375.34051
[7] Elbert, Á.: A half-linear second order differential equation. Qualitative theory of differential equations, Vol. I, II (Szeged, 1979), Colloq. Math. Soc. János Bolyai, 30, North-Holland, Amsterdam, New York, 1981, pp. 153–180. MR 0680591 | Zbl 0511.34006
[8] Elbert, Á., Schneider, A.: Perturbations of the half-linear Euler differential equation. Results Math. 37 (2000), 56–83. DOI 10.1007/BF03322512 | MR 1742294 | Zbl 0958.34029
[9] Hartman, P.: Ordinary Differential Equations. John Willey and Sons, Inc., New York, London, Sydney, 1974. MR 0171038
[10] 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). MR 2144761 | Zbl 1154.34300
Search
Partner of
