Oscillation theorems of comparison type for neutral nonlinear functional differential equations

Grace, S. R.

Czechoslovak Mathematical Journal, Tome 45 (1995) no. 4, pp. 609-626

Détail

DOI : 10.21136/CMJ.1995.128562

Classification : 34C10, 34K11, 34K15, 34K40

Bibliographie

[1] K.E. Foster and R.C. Grimmer: Nonoscillatory solutions of higher order delay differential equations. J. Math. Anal. Appl. 77 (1980), 150–164. | DOI | MR

[2] S.R. Grace: Oscillation of even order nonlinear functional differential equations with deviating arguments. Funkcialaj Ekvacioj 32 (1989), 265–272. | MR | Zbl

[3] S.R. Grace, B.S. Lalli and C.C. Yeh: Oscillation theorems for nonlinear second order differential equations with a nonlinear damping term. SIAM J. Math. Anal. 15 (1984), 1082–1093. | DOI | MR

[4] S.R. Grace and B.S. Lalli: Oscillation theorems for certain neutral differential equations. Czech. Math. J. 38 (1988), 745–753. | MR

[5] S.R. Grace and B.S. Lalli: Oscillation of nonlinear second order neutral delay differential equations. Radovi Mat. 3 (1987), 77–84. | MR

[6] M.K. Grammatikopoulos, G. Ladas and A. Meimaridou: Oscillation and asymptotic behavior of higher order neutral differential equations with variable coefficients. Chines Ann. Math., Ser. B 9 (1988), 322–338. | MR

[7] J. Jaros and T. Kusano: Oscillation theory of higher order linear functional differential equations of neutral type. Hiroshima Math. J. 18 (1988), 509–531. | DOI | MR

[8] J. Jaros and T. Kusano: Sufficient conditions for oscillations in higher linear functional differential equations of neutral type. Japan J. Math. 15 (1989), 501–531. | DOI

[9] A.G. Kartsatos: Maintence of oscillations under the effect of a periodic forcing term. Amer. Math. Soc. 33 (1972), 377–383. | DOI | MR

[10] I.T. Kiguradze: On the oscillations of equation $u^{(m)}+a(t)|u|^nu=0$. Mat. Sb. 65 (1964), 172–187. (Russian) | Zbl

[11] K. Kreith: PDE Generalization of Sturm comparison theorem. Memories Amer. Math. Soc. 48 (1984), 31–46. | MR

[12] M.K. Kwong and J.S.W. Wong: Linearization of second order nonlinear oscillation theorems. Trans. Amer. Math. Soc. 279 (1983), 705–722. | DOI | MR

[13] G. Ladas and Y.G. Sficas: Oscillation of higher order neutral equations. J. Austral. Math. Soc., Ser. B 27 (1986), 502–511. | DOI | MR

[14] W.E. Mahfoud: Remarks on some oscillation theorems for $n^{\text{th}}$ order differential equations with retarded argument. J. Math. Anal. Appl. 62 (1978), 68–80. | DOI | MR

[15] Ch.G. Philos: A new criterion for the oscillatory and asymptotic behavior of delay differential equations. Bull. Acad. Pol. Sci., Ser. Sci. Mat. XXIX (1981), 367–370. | MR | Zbl

[16] Ch.G. Philos: On the existence of nonoscillatory solutions tending to zero at $\infty $ for differential equations with positive delays. Arch. Math. 36 (1980), 168–178. | DOI | MR

[17] Ch.G. Philos and Y.G. Sficas: Oscillatory and asymptotic behavior of second and third order retarded differential equations. Czech. Math. J. 24 (1982), 169–182. | MR

[18] J.S.W. Wong: Second order nonlinear forced oscillations. SIAM J. Math. Anal. 19 (1988), 667–675. | DOI | MR | Zbl