On the behavior of solutions of sublinear second order differential equations

Author:
Hugo Teufel

Journal:
Proc. Amer. Math. Soc. **32** (1972), 445-451

MSC:
Primary 34C99

MathSciNet review:
0294773

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The equations in question generalize

**[1]**Paul B. Bailey, Lawrence F. Shampine, and Paul E. Waltman,*Nonlinear two point boundary value problems*, Mathematics in Science and Engineering, Vol. 44, Academic Press, New York-London, 1968. MR**0230967****[2]**S. Belohorec,*Oscillatory solutions of certain nonlinear differential equations of the second order*, Mat.-Fyz. Časopis Sloven. Akad. Vied**11**(1961), 250-255.**[3]**Štefan Belohorec,*Two remarks on the properties of solutions of a nonlinear differential equation*, Acta Fac. Rerum Natur. Univ. Comenian. Math.**22**(1969), 19–26. MR**0289855****[4]**R. C. Grimmer and Paul Waltman,*A comparison theorem for a class of nonlinear differential inequalities*, Monatsh. Math.**72**(1968), 133–136. MR**0227581****[5]**Philip Hartman,*Ordinary differential equations*, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR**0171038****[6]**J. W. Heidel,*A nonoscillation theorem for a nonlinear second order differential equation*, Proc. Amer. Math. Soc.**22**(1969), 485–488. MR**0248396**, 10.1090/S0002-9939-1969-0248396-0**[7]**J. W. Heidel,*Uniqueness, continuation, and nonoscillation for a second order nonlinear differential equation*, Pacific J. Math.**32**(1970), 715–721. MR**0259244****[8]**J. W. Heidel,*Rate of growth of nonoscillatory solutions for the differential equation 𝑦+𝑞(𝑡)𝑦^{𝛾}𝑠𝑔𝑛𝑦=0, 0<𝛾<1*, Quart. Appl. Math.**28**(1971), 601–606. MR**0301288****[9]**J. W. Heidel and Don B. Hinton,*The existence of oscillatory solutions for a nonlinear differential equation*, SIAM J. Math. Anal.**3**(1972), 344–351. MR**0340721****[10]**Richard A. Moore and Zeev Nehari,*Nonoscillation theorems for a class of nonlinear differential equations*, Trans. Amer. Math. Soc.**93**(1959), 30–52. MR**0111897**, 10.1090/S0002-9947-1959-0111897-8**[11]**H. Teufel, Jr.,*Estimation and extension for nonlinear oscillators*(to appear).

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
34C99

Retrieve articles in all journals with MSC: 34C99

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0294773-1

Keywords:
Comparison,
uniqueness,
second order,
nonlinear,
initial value problem,
boundary value problem,
zeros,
oscillation,
singular solutions,
positive solutions,
Emden-Fowler equation

Article copyright:
© Copyright 1972
American Mathematical Society