Nonlinear oscillation of a sublinear delay equation of arbitrary order

Authors:
Takaŝi Kusano and Hiroshi Onose

Journal:
Proc. Amer. Math. Soc. **40** (1973), 219-224

MSC:
Primary 34K15

DOI:
https://doi.org/10.1090/S0002-9939-1973-0324177-5

MathSciNet review:
0324177

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Abstract | References | Similar Articles | Additional Information

Abstract: The equations considered generalize

**[1]**F. Burkowski,*Nonlinear oscillation of a second order sublinear functional differential equation*, SIAM J. Appl. Math.**21**(1971), 486-490. MR**0308557 (46:7671)****[2]**H. E. Gollwitzer,*On nonlinear oscillation for a second order delay equation*, J. Math. Anal. Appl.**26**(1969), 385-389. MR**39**#581. MR**0239224 (39:581)****[3]**T. G. Hallam,*Asymptotic behavior of the solutions of an th order nonhomogeneous ordinary differential equation*, Trans. Amer. Math. Soc.**122**(1966), 177-194. MR**32**#6000. MR**0188562 (32:6000)****[4]**I. T. Kiguradze,*On the question of variability of solutions of nonlinear differential equations*. Differenciarnye Uravnenija**1**(1965), 995-1006 = Differential Equations**1**(1965), 773-782. MR**33**#2896. MR**0194689 (33:2896)****[5]**T. Kusano and H. Onose,*Oscillation of solutions of nonlinear differential delay equations of arbitrary order*, Hiroshima Math. J.**2**(1972), 1-13. MR**0324175 (48:2527)****[6]**-,*Oscillation theorems for delay equations of arbitrary order*, Hiroshima Math. J.**2**(1972), 263-270. MR**0324176 (48:2528)****[7]**G. Ladas,*Oscillation and asymptotic behavior of solutions of differential equations with retarded argument*, J. Differential Equations**10**(1971), 281-290. MR**0291590 (45:681)****[8]**I. Ličko and M. Švec,*Le caractère oscillatoire des solutions de l'équation*, Czechoslovak Math. J.**13 (88)**(1963), 481-491. MR**28**#4210. MR**0161001 (28:4210)****[9]**G. H. Ryder and D. V. V. Wend,*Oscillation of solutions of certain ordinary differential equations of th order*, Proc. Amer. Math. Soc.**25**(1970), 463-469. MR**41**#5710. MR**0261091 (41:5710)****[10]**V. N. Ševelo and O. N. Odarič,*Certain questions of the theory of oscillation (nonoscillation) of solutions of second order differential equations with retarded argument*, Ukrain. Mat. Ž.**23**(1971), 508-516. (Russian) MR**44**#7088. MR**0289901 (44:7088)****[11]**V. N. Ševelo and N. V. Vareh,*On oscillability of solutions of higher order linear differential equations with retarded argument*, Ukrain. Mat. Ž.**24**(1972), 513-520. (Russian) MR**0308562 (46:7676)****[12]**Y. P. Singh,*The asymptotic behavior of solutions of a nonlinear th-order differential equation*, Okayama Math. J.**15**(1971), 71-73. MR**0301312 (46:470)****[13]**P. Waltman,*On the asymptotic behavior of solutions of an th order equation*, Monatsh. Math.**69**(1965), 427-430. MR**32**#2686. MR**0185217 (32:2686)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1973-0324177-5

Keywords:
Oscillatory,
nonoscillatory,
sublinear,
nonlinear delay equation

Article copyright:
© Copyright 1973
American Mathematical Society