CONTINUATION THEOREMS FOR AMBROSETTI-PRODI TYPE PERIODIC PROBLEMS
2000 ◽
Vol 02
(01)
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pp. 87-126
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Keyword(s):
A Priori
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We study the existence of periodic solutions u(·) for a class of nonlinear ordinary differential equations depending on a real parameter s and obtain the existence of closed connected branches of solution pairs (u, s) to various classes of problems, including some cases, like the superlinear one, where there is a lack of a priori bounds. The results are obtained as a consequence of a new continuation theorem for the coincidence equation Lu=N(u, s) in normed spaces. Among the applications, we discuss also an example of existence of global branches of periodic solutions for the Ambrosetti–Prodi type problem u″+g(u)=s+ p(t), with g satisfying some asymmetric conditions.
On the existence of periodic solutions for the third-order nonlinear ordinary differential equations
1999 ◽
Vol 14
(2)
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pp. 125-130
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1974 ◽
Vol 16
(1)
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pp. 186-199
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1992 ◽
Vol 171
(2)
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pp. 395-406
1976 ◽
Vol 22
(2)
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pp. 467-477
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2010 ◽
Vol 47
(3)
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pp. 573-583
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