Oscillation of a forced second order nonlinear differential equation

Author:
Samuel M. Rankin

Journal:
Proc. Amer. Math. Soc. **59** (1976), 279-282

MSC:
Primary 34C10

MathSciNet review:
0414997

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Sufficient conditions are given which insure that every solution of has arbitrarily large zeros. We seem to have a partial answer to a question posed by Kartsatos [**4**]. An example is given illustrating the result.

**[1]**John R. Graef and Paul W. Spikes,*Asymptotic behavior of solutions of a second order nonlinear differential equation*, J. Differential Equations**17**(1975), 461–476. MR**0361275****[2]**Michael E. Hammett,*Nonoscillation properties of a nonlinear differential equation*, Proc. Amer. Math. Soc.**30**(1971), 92–96. MR**0279384**, 10.1090/S0002-9939-1971-0279384-5**[3]**Athanassios G. Kartsatos,*On the maintenance of oscillations of 𝑛th order equations under the effect of a small forcing term*, J. Differential Equations**10**(1971), 355–363. MR**0288358****[4]**Athanassios G. Kartsatos,*Maintenance of oscillations under the effect of a periodic forcing term*, Proc. Amer. Math. Soc.**33**(1972), 377–383. MR**0330622**, 10.1090/S0002-9939-1972-0330622-0**[5]**Marvin S. Keener,*On the solutions of certain linear nonhomogeneous second-order differential equations*, Applicable Anal.**1**(1971), no. 1, 57–63. MR**0281997****[6]**Stig-Olof Londen,*Some nonoscillation theorems for a second order nonlinear differential equation*, SIAM J. Math. Anal.**4**(1973), 460–465. MR**0333342****[7]**Samuel M. Rankin III,*Oscillation theorems for second-order nonhomogeneous linear differential equations*, J. Math. Anal. Appl.**53**(1976), no. 3, 550–553. MR**0402186****[8]**Alexandra Skidmore and John J. Bowers,*Oscillatory behavior of solutions of 𝑦′′+𝑝(𝑥)𝑦=𝑓(𝑥)*, J. Math. Anal. Appl.**49**(1975), 317–323. MR**0357973****[9]**Alexandra Skidmore and Walter Leighton,*On the differential equation 𝑦′′+𝑝(𝑥)𝑦=𝑓(𝑥)*, J. Math. Anal. Appl.**43**(1973), 46–55. MR**0315213****[10]**S. C. Tefteller,*Oscillation of second order nonhomogeneous linear differential equations*, SIAM J. Appl. Math.**31**(1976), no. 3, 461–467. MR**0450681****[11]**Hugo Teufel Jr.,*Forced second order nonlinear oscillation*, J. Math. Anal. Appl.**40**(1972), 148–152. MR**0313583**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
34C10

Retrieve articles in all journals with MSC: 34C10

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1976-0414997-3

Keywords:
Nonoscillatory solution,
oscillatory solution,
oscillation,
nonlinear forced differential equations

Article copyright:
© Copyright 1976
American Mathematical Society