Hille-Wintner type comparison kriteria for half-linear second order differential equations
Došlý, Ondřej ; Pátíková, Zuzana
Archivum Mathematicum, Tome 042 (2006), p. 185-194 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

We establish Hille-Wintner type comparison criteria for the half-linear second order differential equation \[ \left(r(t)\Phi (x^{\prime })\right)^{\prime }+c(t)\Phi (x)=0,\quad \Phi (x)=|x|^{p-2}x\,,\ p>1\,, \] where this equation is viewed as a perturbation of another equation of the same form.

Publié le : 2006-01-01
Classification:  34C10,  34C15 
@article{107995,
     author = {Ond\v rej Do\v sl\'y and Zuzana P\'at\'\i kov\'a},
     title = {Hille-Wintner type comparison kriteria for half-linear second order differential equations},
     journal = {Archivum Mathematicum},
     volume = {042},
     year = {2006},
     pages = {185-194},
     zbl = {1164.34386},
     mrnumber = {2240356},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107995}
}

Došlý, Ondřej; Pátíková, Zuzana. Hille-Wintner type comparison kriteria for half-linear second order differential equations. Archivum Mathematicum, Tome 042 (2006) pp. 185-194. http://gdmltest.u-ga.fr/item/107995/

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. | MR 2091751

Došlý O. A remark on conjugacy of half-linear second order differential equations, Math. Slovaca 50 (2000), 67–79. | MR 1764346 | Zbl 0959.34025

Došlý O. Half-Linear Differential Equations, Handbook of Differential Equations: Ordinary Differential Equations, Vol. I, A. Cañada, P. Drábek, A. Fonda ed., Elsevier, Amsterdam, 2004, 161–357. | MR 2166491 | Zbl 1231.34059

Došlý O.; Lomtatidze A. Oscillation and nonoscillation criteria for half-linear second order differential equations, to appear in Hiroshima Math. J. | MR 2259737 | Zbl 1123.34028

Došlý O.; Peňa S. A linearization method in oscillation theory of half-linear differential equations, to appear in J. Inequal. Appl. | MR 2211857

Došlý O.; Řezníčková J. Regular half-linear second order differential equations, Arch. Math. (Brno) 39 (2003), 233–245. | MR 2010724 | Zbl 1119.34029

Elbert Á.; Kusano T. Principal solutions of nonoscillatory half-linear differential equations, Adv. Math. Sci. Appl. 18 (1998), 745–759. (1998)

Elbert Á.; Schneider A. Perturbations of the half-linear Euler differential equation, Results Math. 37 (2000), 56–83. | MR 1742294 | Zbl 0958.34029

Jaroš J.; Kusano T. A Picone type identity for half-linear differential equations, Acta Math. Univ. Comenian. 68 (1999), 137–151. (1999) | MR 1711081

Kusano T.; Yosida N. Nonoscillation theorems for a class of quasilinear differential equations of second order, Acta Math. Hungar. 76 (1997), 81–89. (1997)

Kusano T.; Yosida N.; Ogata A. Strong oscillation and nonoscillation of quasilinear differential equations of second order, Differential Equations Dynam. Systems 2 (1994), 1–10. (1994) | MR 1386034

Mirzov J. D. Principal and nonprincipal solutions of a nonoscillatory system, Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 31 (1988), 100–117. (1988) | MR 1001343

Řezníčková J. Half-linear Hartman-Wintner theorems, Stud. Univ. Žilina Math. Phys. Ser. 15 (2002), 56–66. | MR 1980763 | Zbl 1051.34026

Řezníčková J. An oscillation criterion for half-linear second order differential equations, Miskolc Math. Notes 5 (2004), 203–212. | MR 2091995 | Zbl 1150.34010

Sugie J.; Yamaoka N. Growth conditions for oscillation of nonlinear differential equations with $p$-Laplacian, J. Math. Anal. Appl. 305 (2005), 18–34. | MR 2132886 | Zbl 1085.34029