A boundedness theorem for non-linear differential equations of the second order
1951 ◽
Vol 47
(1)
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pp. 49-54
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Keyword(s):
1. This paper deals with the differential equation(dots denoting derivatives with respect to t), where for large x the ‘restoring force’ term g(x) has the sign of x and the ‘damping factor’ kf(x) is positive on the average. It will be shown that every solution of (1) ultimately (for sufficiently large t) satisfieswith B independent of k. The conditions on f(x), g(x) and p(t) (stated in §§ 2, 3) are rather milder than those assumed by Cartwright and Littlewood (1, 2) and Newman (3) in proving similar results.
1920 ◽
Vol 39
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pp. 21-24
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1931 ◽
Vol 27
(4)
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pp. 546-552
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1951 ◽
Vol 3
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pp. 335-338
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1914 ◽
Vol 33
◽
pp. 2-13
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1955 ◽
Vol 51
(4)
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pp. 604-613
2018 ◽
Vol 12
(2)
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pp. 481-492
1965 ◽
Vol 14
(4)
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pp. 257-268
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2020 ◽
Vol 8
(3)
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pp. 61-68