Remarks on nonoscillation theorems for a second order nonlinear differential equation

Author:
James S. W. Wong

Journal:
Proc. Amer. Math. Soc. **83** (1981), 541-546

MSC:
Primary 34C10

DOI:
https://doi.org/10.1090/S0002-9939-1981-0627687-0

MathSciNet review:
627687

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper proves two results concerning nonoscillation of solutions of the second order nonlinear differential equation ()

*Let*.

*If*,

*then*()

*is nonoscillatory*. Theorem B.

*Let*.

*If*,

*then*()

*is nonoscillatory*.

**[1]**F. V. Atkinson,*On second order nonlinear oscillations*, Pacific J. Math.**5**(1955), 643-647. MR**0072316 (17:264e)****[2]**M. Bôcher,*The theorems of oscillation of Sturm and Klein*. I, II, Bull. Amer. Math. Soc.**4**(1897/8), 295-313; 365-376.**[3]**C. V. Coffman and D. F. Ullrich,*On the continuation of solutions of a certain nonlinear differential equation*, Monatsh. Math.**71**(1967), 385-392. MR**0227494 (37:3078)****[4]**C. V. Coffman and J. S. W. Wong,*Oscillation and nonoscillation of solutions of generalized Emden-Fowler equations*, Trans. Amer. Math. Soc.**167**(1972), 399-434. MR**0296413 (45:5473)****[5]**-,*Oscillation and nonoscillation theorems for second order ordinary differential equations*, Funkcial. Ekvac.**15**(1972), 119-130. MR**0333337 (48:11662)****[6]**M. E. Gollwitzer,*Nonoscillation theorems for a nonlinear differential equation*, Proc. Amer. Math. Soc.**26**(1970), 78-84. MR**0259243 (41:3885)****[7]**J. W. Heidel,*A nonoscillation theorem for a nonlinear second order differential equation*, Proc. Amer. Math. Soc.**22**(1969), 485-488. MR**0248396 (40:1648)****[8]**D. V. Izyumova and I. T. Kiguradze,*Some remarks on the solutions of the equation*, Differencial'nye Uravnenija**4**(1968), 589-605. (Russian) MR**0227544 (37:3128)****[9]**A. Kneser,*Untersuchung über die reellen Nullstellen der Integrale linear Differentialgleichungen*, Math. Ann.**42**(1893), 409-435. MR**1510784****[10]**W. Leighton,*On self-adjoint differential equation of second order*, J. London Math. Soc.**27**(1952), 37-47. MR**0046506 (13:745b)****[11]**J. S. W. Wong,*On the generalized Emden-Fowler equation*, SIAM Rev.**17**(1975), 339-360. MR**0367368 (51:3610)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0627687-0

Keywords:
Second order,
nonlinear,
differential equation,
oscillation

Article copyright:
© Copyright 1981
American Mathematical Society