Continuation theorems for Ambrosetti-Prodi type periodic problems
(2000) Communications in Contemporary Mathematics — Vol. 2, n° 1, p. 87-126 (2000)
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- Abstract
- 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.
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Mawhin, J., Rebelo, C., & Zanolin, F. (2000). Continuation theorems for Ambrosetti-Prodi type periodic problems. Communications in Contemporary Mathematics, 2(1), 87-126. https://hdl.handle.net/2078.5/139826 (Original work published 2000)