A remark on the linearization technique in half-linear oscillation theory

• Autorzy: Dosly O.
• Języki publikacji: EN

Abstrakty

EN

We show that oscillatory properties of the half-linear second order differential equation (r(t)Φ(x'))' + c(t)Φ(x) = 0, Φ(x) = |x|p-2x, p > 1, can be investigated via oscillatory properties of a certain associated second order linear differential equation. In contrast to paper [6], we do not need to distinguish between the cases p ≥ 2 and p ∈ (1, 2]. Our results also improve the oscillation and nonoscillation criteria given in [4].

Słowa kluczowe

EN

half-linear oscillation theory; oscillation and nonoscillation criteria; Riccati technique; perturbation principle

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2006
• Tom: Vol. 26, no. 2
• Strony: 305--315
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Dosly O.

• Masaryk University, Department of Mathematics, Janáčkovo nám. 2a, CZ-662 95 Brno,

Bibliografia

• [1] Agarwal R. P., Grace S.R., O'Regan D., Oscillation Theory of Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations, Kluwer Academic Publishers, Dordrecht/Boston/London, 2002.
• [2] Dosly O., Oscillation criteria for half-linear second order differential equations, Hiroshima Math. J. 28 (1998), 507-521.
• [3] Dosly O., Half-Linear Differential Equations, Handbook of Differential Equations: Ordinary Differential Equations, Vol. I, Canada A., Drabek P., Fonda A. ed., Elsevier, Amsterdam, 2004, 161-357.
• [4] Dosly O., Lomtatidze A., Oscillation and nonoscillation criteria for half-linear second order differential equations, to appear in Hiroshima Math. J.
• [5] Dosly O., Patikova Z., Hille-Wintner type comparison criteria for half-linear second order differential equations, Arch. Math. (Brno) 42 (2006), 186-194.
• [6] Dosly O., Pena, A linearization method in oscillation theory of half-linear differential equations, in J. Inequal. Appl. 2005 (2005), 235-245.
• [7] Dosly O., Rehak P., Half-Linear Differential Equations, North-Holland Mathematics Studies 202, Elsevier, Amsterdam, 2005.
• [8] Dosly O., Reznickova J., Regular half-linear second order differential equations, Arch. Math. (Brno) 39 (2003), 233-245.
• [9] Elbert A., A half-linear second order differential equation, Colloq. Math. Soc. Janos Bolyai 30 (1979), 153-180.
• [10] Elbert A., Oscillation and nonoscillation theorems for some non-linear ordinary differential equations, Lectures Notes in Math. 964 (1982), 187-212.
• [11] Elbert A., A. Schneider, Perturbations of the half-linear Euler differential equation, Result. Math. 37 (2000), 56-83.
• [12] Sugie J., Yamaoka N., Growth conditions for oscillation of nonlinear differential equations with p-Laplacian, J. Math. Anal. Appl. 305 (2005), 18-34.
• [13] Swanson C.A., Comparison and Oscillation Theory of Linear Differential Equations, Acad. Press, New York-London, 1968.