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- W2057199003 abstract "In this paper the Duffing-type equation ( d 2 x / dt 2 )+ x 2 n +1 + p 2 n ( t ) x 2 n +…+ p 1 ( t ) x + p 0 ( t )=0 is studied where the p j 's are 1-periodic. It is shown that all solutions of this equation are bounded, provided that the p j ( t ) (0⩽ j ⩽ n ) are of bounded variation in [0, 1] and that the derivatives of p j ( t ) ( n ⩽ j ⩽2 n ) are Lipschitzian. It is also shown that there exist p j 's being discontinuous everywhere such that all solutions of the equation are bounded. This implies that the continuity of p j 's is not necessary for the boundedness of solutions of the equation." @default.
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- W2057199003 date "2000-01-01" @default.
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- W2057199003 title "Lagrange Stability for Duffing-Type Equations" @default.
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- W2057199003 doi "https://doi.org/10.1006/jdeq.1999.3663" @default.
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