On linear ordinary differential equations with exponential coefficients
Author:
G. A. Hegemier
Journal:
Quart. Appl. Math. 26 (1968), 389-401
MSC:
Primary 34.50
DOI:
https://doi.org/10.1090/qam/235211
MathSciNet review:
235211
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Abstract: A system of linear ordinary differential equations with exponential coefficients is considered; several theorems are presented concerning general solutions and their asymptotic forms for large values of the independent variable; elementary examples are given and applications cited to illustrate, and demonstrate the utility of, the solution forms obtained. The relevance of the results to the solution of problems of structural stability and wave propagation is briefly discussed.
- K. G. Valeev, On linear differential equations with exponential coefficients and stationary delays of the argument. Regular case, J. Appl. Math. Mech. 26 (1962), 668–677. MR 0144045, DOI https://doi.org/10.1016/0021-8928%2862%2990035-7
- K. G. Valeev, On linear differential equations with exponential coefficients and stationary lags in the argument. Irregular case, J. Appl. Math. Mech. 26 (1962), 1536–1553. MR 0150428, DOI https://doi.org/10.1016/0021-8928%2862%2990191-0
G. A. Hegemier, Instability of cylindrical shells subjected to axisymmetic moving loads, J. Appl. Mech. 33, 289-296 (1966)
G. A. Hegemier, Stability of cylindrical shells under moving loads by the direct method of Liapunov, J. of Appl. Mech., Paper No. 67-WA 1APM-3
- L. A. Liusternik and V. J. Sobolev, Elements of functional analysis, Russian Monographs and Texts on Advanced Mathematics and Physics, Vol. 5, Hindustan Publishing Corp., Delhi; Gordon and Breach Publishers, Inc., New York, 1961. MR 0141967
G. A. Hegemier and L. W. Morland, Stress waves in a temperature dependent viscoelastic half-space subjected to impulsive electromagnetic radiation, Tech. Rpt. No. 4, AF-AFSOR-1226-67, Dept. of the Aerospace and Mechanical Engineering Sciences, Univ. of California, San Diego (to appear)
G. A. Hegemier and L. W. Morland, One-dimensional wave solutions for a nonhomogeneous semi-infinite medium, Tech. Rpt. No. 5, AF-AFOSR-1226-67, Dept. of the Aerospace and Mechanical Engineering Sciences, Univ. of California, San Diego, (to appear)
K. G. Valeev, On linear differential equations with exponential coefficients and stationary delays of the argument. Regular case, PMM 26, No. 2, 1536–1553 (1962)
K. G. Valeev, On linear differential equations with exponential coefficients and stationary lags in the argument. Irregular case, PMM 26, No. 6, 1012-1024 (1962)
G. A. Hegemier, Instability of cylindrical shells subjected to axisymmetic moving loads, J. Appl. Mech. 33, 289-296 (1966)
G. A. Hegemier, Stability of cylindrical shells under moving loads by the direct method of Liapunov, J. of Appl. Mech., Paper No. 67-WA 1APM-3
L. Linsternik and V. Sobolev, Elements of functional analysis, New York, Frederick Ungar Publishing Co., 1961
G. A. Hegemier and L. W. Morland, Stress waves in a temperature dependent viscoelastic half-space subjected to impulsive electromagnetic radiation, Tech. Rpt. No. 4, AF-AFSOR-1226-67, Dept. of the Aerospace and Mechanical Engineering Sciences, Univ. of California, San Diego (to appear)
G. A. Hegemier and L. W. Morland, One-dimensional wave solutions for a nonhomogeneous semi-infinite medium, Tech. Rpt. No. 5, AF-AFOSR-1226-67, Dept. of the Aerospace and Mechanical Engineering Sciences, Univ. of California, San Diego, (to appear)
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Article copyright:
© Copyright 1968
American Mathematical Society
