Stability results for periodic second order linear differential equations

Erbe, L. H.

doi:10.1090/S0002-9939-1985-0770535-2

Stability results for periodic second order linear differential equations
HTML articles powered by AMS MathViewer

by L. H. Erbe PDF

Proc. Amer. Math. Soc. 93 (1985), 272-276 Request permission

Abstract:

Sufficient conditions for stability, asymptotic stability and instability of the trivial solution of a periodic second order linear differential equation are obtained.

References

L. H. Erbe, Third order linear differential equations with periodic coefficients, Proc. Amer. Math. Soc. 64 (1977), no. 2, 241–247. MR 454208, DOI 10.1090/S0002-9939-1977-0454208-7
L. Erbe, Stability and periodicity for linear differential equations with periodic coefficients, Ann. Polon. Math. 31 (1975), no. 2, 131–140. MR 417508, DOI 10.4064/ap-31-2-131-140
Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038
A. M. Liapunov, Stability of motion, Mathematics in Science and Engineering, Vol. 30, Academic Press, New York-London, 1966. With a contribution by V. A. Pliss and an introduction by V. P. Basov; Translated from the Russian by Flavian Abramovici and Michael Shimshoni. MR 0208093
G. A. 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 0218688
Wilhelm Magnus and Stanley Winkler, Hill’s equation, Interscience Tracts in Pure and Applied Mathematics, No. 20, Interscience Publishers John Wiley & Sons, New York-London-Sydney, 1966. MR 0197830
Richard A. Moore, The least eigenvalue of Hill’s equation, J. Analyse Math. 5 (1956/57), 183–196. MR 86200, DOI 10.1007/BF02937345
Z. Opial, Sur une inégalité de C. de la Vallée Poussin dans la théorie de l’équation différentielle linéaire du second ordre, Ann. Polon. Math. 6 (1959/60), 87–91 (French). MR 104875, DOI 10.4064/ap-6-1-87-91
E. L. Tonkov and G. I. Jutkin, Periodic solutions, and stability of a linear differential equation with periodic coefficients, Differencial′nye Uravnenija 5 (1969), 1990–2001 (Russian). MR 0254347