Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Third order linear differential equations with periodic coefficients


Author: L. H. Erbe
Journal: Proc. Amer. Math. Soc. 64 (1977), 241-247
MSC: Primary 34D35
DOI: https://doi.org/10.1090/S0002-9939-1977-0454208-7
MathSciNet review: 0454208
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The third order linear differential equation $ Ly = y''' + {p_2}(t)y'' + {p_1}(t)y' + {p_0}(t)y = 0$ is studied, where $ {p_i}(t)$ are continuous real-valued and periodic of period $ \omega > 0$. Various criteria are obtained which guarantee ``partial'' asymptotic stability or instability by means of effective bounds on the Floquet characteristic multipliers of $ Ly = 0$.


References [Enhancements On Off] (What's this?)

  • [1] W. A. Coppel, Disconjugacy, Lecture Notes in Math., vol. 220, Springer-Verlag, Berlin and New York, 1971. MR 0460785 (57:778)
  • [2] L. Erbe, Stability and periodicity for linear differential equations with periodic coefficients, Ann. Polon. Math. 31 (1975), 131-140. MR 0417508 (54:5558)
  • [3] -, Disconjugacy conditions for the third order linear differential equation, Canad. Math. Bull. 12 (1969), 603-613. MR 40 #5972. MR 0252755 (40:5972)
  • [4] P. Hartman, On disconjugacy criteria, Proc. Amer. Math. Soc. 24 (1970), 374-381. MR 40 #4535. MR 0251304 (40:4535)
  • [5] L. K. Jackson, Disconjugacy conditions for linear third-order differential equations, J. Differential Equations 4 (1968), 369-372. MR 36 # 1702. MR 0226112 (37:1702)
  • [6] G. D. Jones, An asymptotic property of solutions of $ y''' + py' + qy = 0$, Pacific J. Math. 47 (1973), 135-138. MR 48 #4410. MR 0326065 (48:4410)
  • [7] A. Lasota, Sur la distance entre les zéros de l'équation différentielle linéaire du troisième ordre, Ann. Polon. Math. 13 (1963), 129-132. MR 28 #4181. MR 0160972 (28:4181)
  • [8] A. C. Lazer, The behavior of solutions of the differential equation $ y''' + p(x)y' + q(x)y = 0$, Pacific J. Math. 17 (1966), 435-466. MR 33 #1552. MR 0193332 (33:1552)
  • [9] A. Yu. Levin, On some estimates of a differential function, Dokl. Akad. Nauk SSSR 138 (1961), 37-38 = Soviet Math. Dokl. 2 (1961), 523-524. MR 23 #A3310. MR 0126013 (23:A3310)
  • [10] G. P. Los', A sufficient test for the stability of the trivial solution of a third order differential equation with periodic coefficients, Differencial'nye Uravnenija 3 (1967), 1707-1717. (Russian) MR 36 # 1772. MR 0218688 (36:1772)
  • [11] V. Seda, On the three-point boundary-value problem for a non-linear third order ordinary differential equation, Arch. Math. (Brno) 8 (1972), 85-98 (1973). MR 48 #619. MR 0322257 (48:619)
  • [12] E. L. Tonkov and G. I. Yutkin, Periodic solutions, and stability of a linear differential equation with periodic coefficients, Differencial'nye Uravnenija 5 (1969), 1990-2001 = Differential Equations 5 (1969), 1484-1492. MR 40 #7556. MR 0254347 (40:7556)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34D35

Retrieve articles in all journals with MSC: 34D35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0454208-7
Keywords: Periodic solution, Floquet theory, characteristic multipliers, disconjugacy, oscillation
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society