Oscillation and nonoscillation of solutions of second order linear differential equations with integrable coefficients
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- by James S. W. Wong PDF
- Trans. Amer. Math. Soc. 144 (1969), 197-215 Request permission
References
- John H. Barrett, Disconjugacy of second-order linear differential equations with nonnegative coefficients, Proc. Amer. Math. Soc. 10 (1959), 552–561. MR 108613, DOI 10.1090/S0002-9939-1959-0108613-8 W. J. Coles, An oscillation criterion for second order linear differential equations, Proc Amer. Math. Soc. 19 (1968), 755-759.
- W. J. Coles, A simple proof of a well-known oscillation theorem, Proc. Amer. Math. Soc. 19 (1968), 507. MR 223644, DOI 10.1090/S0002-9939-1968-0223644-0
- W. J. Coles and D. Willett, Summability criteria for oscillation of second order linear differential equations, Ann. Mat. Pura Appl. (4) 79 (1968), 391–398. MR 236462, DOI 10.1007/BF02415185
- William Benjamin Fite, Concerning the zeros of the solutions of certain differential equations, Trans. Amer. Math. Soc. 19 (1918), no. 4, 341–352. MR 1501107, DOI 10.1090/S0002-9947-1918-1501107-2
- Philip Hartman, On non-oscillatory linear differential equations of second order, Amer. J. Math. 74 (1952), 389–400. MR 48667, DOI 10.2307/2372004
- Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038
- Einar Hille, Non-oscillation theorems, Trans. Amer. Math. Soc. 64 (1948), 234–252. MR 27925, DOI 10.1090/S0002-9947-1948-0027925-7
- Adolf Kneser, Untersuchungen über die reellen Nullstellen der Integrale linearer Differentialgleichungen, Math. Ann. 42 (1893), no. 3, 409–435 (German). MR 1510784, DOI 10.1007/BF01444165
- A. Ju. Levin, Classification of the cases of non-oscillation for the equation $\ddot x+p(t)\dot x+q(t)x=0$, where $q(t)$ is of constant sign, Dokl. Akad. Nauk SSSR 171 (1966), 1037–1040 (Russian). MR 0206374
- J. W. Macki and J. S. W. Wong, Oscillation theorems for linear second order ordinary differential equations, Proc. Amer. Math. Soc. 20 (1969), 67–72. MR 235202, DOI 10.1090/S0002-9939-1969-0235202-3
- Lawrence Markus and Richard A. Moore, Oscillation and disconjugacy for linear differential equations with almost periodic coefficients, Acta Math. 96 (1956), 99–123. MR 80813, DOI 10.1007/BF02392359
- Richard A. Moore, The behavior of solutions of a linear differential equation of second order, Pacific J. Math. 5 (1955), 125–145. MR 68690, DOI 10.2140/pjm.1955.5.125
- Richard A. Moore, The least eigenvalue of Hill’s equation, J. Analyse Math. 5 (1956/57), 183–196. MR 86200, DOI 10.1007/BF02937345
- Zeev Nehari, Oscillation criteria for second-order linear differential equations, Trans. Amer. Math. Soc. 85 (1957), 428–445. MR 87816, DOI 10.1090/S0002-9947-1957-0087816-8
- Z. Opial, Sur les intégrales oscillantes de l’équation différentielle $u''+f(t)u=0$, Ann. Polon. Math. 4 (1958), 308–313 (French). MR 97583
- Z. Opial, Sur une critère d’oscillation des intégrales de l’équation différentielle $(Q(t)x’)’+f(t)x=0$, Ann. Polon. Math. 6 (1959/60), 99–104 (French). MR 104876, DOI 10.4064/ap-6-1-99-104 B. Riemann and H. Weber, Die Partiellen Differentialgleichungen der Mathematischen Physik. II, 5th ed., Brunschweig, 1912.
- William T. Reid, Oscillation criteria for linear differential systems with complex coefficients, Pacific J. Math. 6 (1956), 733–751. MR 84655, DOI 10.2140/pjm.1956.6.733
- William T. Reid, Oscillation criteria for self-adjoint differential systems, Trans. Amer. Math. Soc. 101 (1961), 91–106. MR 133518, DOI 10.1090/S0002-9947-1961-0133518-X C. Sturm, Sur les equations differentielles lineaires du second ordre, J. Math. Pures Appl. 1 (1836), 106-186.
- Aurel Wintner, A criterion of oscillatory stability, Quart. Appl. Math. 7 (1949), 115–117. MR 28499, DOI 10.1090/S0033-569X-1949-28499-6
- Aurel Wintner, On the non-existence of conjugate points, Amer. J. Math. 73 (1951), 368–380. MR 42005, DOI 10.2307/2372182
- Aurel Wintner, On the comparison theorem of Kneser-Hille, Math. Scand. 5 (1957), 255–260. MR 96867, DOI 10.7146/math.scand.a-10502
- D. Willett, On the oscillatory behavior of the solutions of second order linear differential equations, Ann. Polon. Math. 21 (1969), 175–194. MR 249723, DOI 10.4064/ap-21-2-175-194
- James S. W. Wong, Second order linear oscillation with integrable coefficients, Bull. Amer. Math. Soc. 74 (1968), 909–911. MR 233010, DOI 10.1090/S0002-9904-1968-12078-6
- James S. W. Wong, On second order nonlinear oscillation, Funkcial. Ekvac. 11 (1968), 207–234 (1969). MR 245915
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 144 (1969), 197-215
- MSC: Primary 34.42
- DOI: https://doi.org/10.1090/S0002-9947-1969-0251305-6
- MathSciNet review: 0251305