Multiplicity results for periodic solutions of second order ODEs with asymmetric nonlinearities
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- by C. Rebelo and F. Zanolin PDF
- Trans. Amer. Math. Soc. 348 (1996), 2349-2389 Request permission
Abstract:
We prove various results on the existence and multiplicity of harmonic and subharmonic solutions to the second order nonautonomous equation $x'' + g(x) = s + w(t,x)$, as $s\to +\infty$ or $s\to - \infty ,$ where $g$ is a smooth function defined on a open interval $]a,b[\subset {\mathbb {R}}.$ The hypotheses we assume on the nonlinearity $g(x)$ allow us to cover the case $b=+\infty$ (or $a = -\infty$) and $g$ having superlinear growth at infinity, as well as the case $b < +\infty$ (or $a > -\infty$) and $g$ having a singularity in $b$ (respectively in $a$). Applications are given also to situations like $g’(-\infty ) \not = g’(+\infty )$ (including the so-called “jumping nonlinearities”). Our results are connected to the periodic Ambrosetti - Prodi problem and related problems arising from the Lazer - McKenna suspension bridges model.References
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Additional Information
- C. Rebelo
- Affiliation: International School for Advanced Studies, via Beirut 2-4, 34013 Trieste, Italy
- Address at time of publication: Centro de Matemática e Aplicações Fundamentais, Av. Prof. Gama Pinto 2, 1699 Lisboa Codex, Portugal
- Email: carlota@ptmat.lmc.fc.ul.pt
- F. Zanolin
- Affiliation: Dipartimento di Matematica e Informatica, Università, via delle Scienze 208 (loc. Rizzi), 33100 Udine, Italy
- MR Author ID: 186545
- Email: zanolin@dimi.uniud.it
- Received by editor(s): August 4, 1994
- Received by editor(s) in revised form: February 28, 1995
- Additional Notes: Work performed in the frame of the EEC project “Non linear boundary value problems: existence, multiplicity and stability of solutions”, grant ERB CHRX-CT94-0555.
The first author is on leave of absence from Faculdade de Ciências da Universidade de Lisboa with a fellowship from Programa Ciência (JNICT).
The second author’s work performed under the auspices of GNAFA-CNR and supported by MURST (40% and 60% funds). - © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 348 (1996), 2349-2389
- MSC (1991): Primary 34C25; Secondary 34B15
- DOI: https://doi.org/10.1090/S0002-9947-96-01580-2
- MathSciNet review: 1344211