Oscillation theorems for systems of linear differential equations
Author:
Zeev Nehari
Journal:
Trans. Amer. Math. Soc. 139 (1969), 339347
MSC:
Primary 34.42
MathSciNet review:
0239185
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
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 J. H. Barrett, Fourth order boundary value problems and comparison theorems, Canad. J. Math. 13 (1961), 625638. MR 0133519 (24:A3350)
 [2]
 E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGrawHill, New York, 1955. MR 0069338 (16:1022b)
 [3]
 P. Hartman, Ordinary differential equations, Wiley, New York, 1964. MR 0171038 (30:1270)
 [4]
 P. Hartman and A. Wintner, On disconjugate differential systems, Canad. J. Math. 8 (1956), 7281. MR 0074595 (17:611h)
 [5]
 R. W. Hunt, The behavior of solutions of ordinary, selfadjoint differential equations of arbitrary even order, Pacific J. Math. 12 (1962), 945961. MR 0147725 (26:5239)
 [6]
 , Oscillation properties of evenorder linear differential equations, Trans. Amer. Math. Soc. 115 (1965), 5461. MR 0203132 (34:2985)
 [7]
 W. J. Kim, Disconjugacy and disfocality of differential systems, J. Math. Anal. Appl. (to appear). MR 0236464 (38:4759)
 [8]
 W. Leighton and Z. Nehari, On the oscillation of solutions of selfadjoint linear differential equations of the fourth order, Trans. Amer. Math. Soc. 89 (1958), 325377. MR 0102639 (21:1429)
 [9]
 A. Ju. Levin, Some questions on the oscillation of solutions of linear differential equations, Dokl. Akad. Nauk SSSR 148 (1963), 512515 = Soviet Math. Dokl. 4 (1963), 121124. MR 0146450 (26:3972)
 [10]
 , Distribution of the zeros of solutions of a linear differential equation, Dokl. Akad. Nauk SSSR 156 (1964), 12811284=Soviet Math. Dokl. 5 (1964), 818821. MR 0164079 (29:1378)
 [11]
 D. London and B. Schwarz, Disconjugacy of complex differential systems and equations, Trans. Amer. Math. Soc. 135 (1969), 487505. MR 0237875 (38:6154)
 [12]
 Z. Nehari, On an inequality of Lyapunov, Studies in mathematical analysis and related topics, pp. 256261, Stanford Univ. Press, Stanford, California, 1962. MR 0145149 (26:2684)
 [13]
 , Disconjugate linear differential operators, Trans. Amer. Math. Soc. 129 (1967), 500516. MR 0219781 (36:2860)
 [14]
 W. T. Reid, Principal solutions of nonoscillatory selfadjoint linear differential equations, Pacific J. Math. 8 (1958), 147169. MR 0098220 (20:4682)
 [15]
 , Oscillation criteria for selfadjoint differential systems, Trans. Amer. Math. Soc. 101 (1961), 91106. MR 0133518 (24:A3349)
 [16]
 B. Schwarz, Disconjugacy of complex differential systems, Trans. Amer. Math. Soc. 125 (1966), 482496. MR 0206371 (34:6190)
 [17]
 T. L. Sherman, Properties of solutions of nth order linear differential equations, Pacific J. Math. 15 (1965), 10451060. MR 0185185 (32:2654)
 [18]
 , Properties of solutions of quasidifferential equations, Duke Math. J. 32 (1965), 297304. MR 0179411 (31:3659)
 [19]
 R. L. Sternberg, Variational methods and nonoscillation theorems for systems of differential equations, Duke Math. J. 19 (1952), 311322. MR 0048668 (14:50c)
 [20]
 H. M. Sternberg and R. L. Sternberg, A twopoint boundary problem for ordinary selfadjoint differential equations of fourth order, Canad. J. Math. 6 (1954), 416419. MR 0061738 (15:874c)
 [21]
 A. Wintner, On the nonexistence of conjugate points, Amer. J. Math. 73 (1951), 368380. MR 0042005 (13:37d)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947196902391856
PII:
S 00029947(1969)02391856
Article copyright:
© Copyright 1969
American Mathematical Society
