Oscillation theorems for systems of linear differential equations

Author:
Zeev Nehari

Journal:
Trans. Amer. Math. Soc. **139** (1969), 339-347

MSC:
Primary 34.42

MathSciNet review:
0239185

Full-text PDF Free Access

References | Similar Articles | Additional Information

**[1]**John H. Barrett,*Fourth order boundary value problems and comparison theorems*, Canad. J. Math.**13**(1961), 625–638. MR**0133519****[2]**Earl A. Coddington and Norman Levinson,*Theory of ordinary differential equations*, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR**0069338****[3]**Philip Hartman,*Ordinary differential equations*, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR**0171038****[4]**Philip Hartman and Aurel Wintner,*On disconjugate differential systems*, Canad. J. Math.**8**(1956), 72–81. MR**0074595****[5]**Robert W. Hunt,*The behavior of solutions of ordinary, self-adjoint differential equations of arbitrary even order*, Pacific J. Math.**12**(1962), 945–961. MR**0147725****[6]**Robert W. Hunt,*Oscillation properties of even-order linear differential equations*, Trans. Amer. Math. Soc.**115**(1965), 54–61. MR**0203132**, 10.1090/S0002-9947-1965-0203132-X**[7]**W. J. Kim,*Disconjugacy and disfocality of differential systems*, J. Math. Anal. Appl.**26**(1969), 9–19. MR**0236464****[8]**Walter Leighton and Zeev Nehari,*On the oscillation of solutions of self-adjoint linear differential equations of the fourth order*, Trans. Amer. Math. Soc.**89**(1958), 325–377. MR**0102639**, 10.1090/S0002-9947-1958-0102639-X**[9]**A. Ju. Levin,*Some questions on the oscillation of solutions of linear differential equations*, Dokl. Akad. Nauk SSSR**148**(1963), 512–515 (Russian). MR**0146450****[10]**A. Ju. Levin,*On the distribution of zeros of solutions of a linear differential equation*, Dokl. Akad. Nauk SSSR**156**(1964), 1281–1284 (Russian). MR**0164079****[11]**David London and Binyamin Schwarz,*Disconjugacy of complex differential systems and equations*, Trans. amer. Math. Soc.**135**(1969), 487–505. MR**0237875**, 10.1090/S0002-9947-1969-0237875-2**[12]**Zeev Nehari,*On an inequality of Lyapunov*, Studies in mathematical analysis and related topics, Stanford Univ. Press, Stanford, Calif., 1962, pp. 256–261. MR**0145149****[13]**Zeev Nehari,*Disconjugate linear differential operators*, Trans. Amer. Math. Soc.**129**(1967), 500–516. MR**0219781**, 10.1090/S0002-9947-1967-0219781-0**[14]**William T. Reid,*Principal solutions of non-oscillatory self-adjoint linear differential systems*, Pacific J. Math.**8**(1958), 147–169. MR**0098220****[15]**William T. Reid,*Oscillation criteria for self-adjoint differential systems*, Trans. Amer. Math. Soc.**101**(1961), 91–106. MR**0133518**, 10.1090/S0002-9947-1961-0133518-X**[16]**Binyamin Schwarz,*Disconjugacy of complex differential systems*, Trans. Amer. Math. Soc.**125**(1966), 482–496. MR**0206371**, 10.1090/S0002-9947-1966-0206371-8**[17]**Thomas L. Sherman,*Properties of solutions of 𝑛𝑡ℎ order linear differential equations*, Pacific J. Math.**15**(1965), 1045–1060. MR**0185185****[18]**T. L. Sherman,*Properties of solutions of quasi-differential equations*, Duke Math. J.**32**(1965), 297–304. MR**0179411****[19]**Robert L. Sternberg,*Variational methods and non-oscillation theorems for systems of differential equations*, Duke Math. J.**19**(1952), 311–322. MR**0048668****[20]**H. M. Sternberg and R. L. Sternberg,*A two-point boundary problem for ordinary self-adjoint differential equations of fourth order*, Canadian J. Math.**6**(1954), 416–419. MR**0061738****[21]**Aurel Wintner,*On the non-existence of conjugate points*, Amer. J. Math.**73**(1951), 368–380. MR**0042005**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
34.42

Retrieve articles in all journals with MSC: 34.42

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1969-0239185-6

Article copyright:
© Copyright 1969
American Mathematical Society