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Existence and multiplicity results for periodic solutions of nonlinear difference equations

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Bereanu, Cristian [UCL] Mawhin, Jean [UCL]

We use Brouwer degree to prove existence and multiplicity results for the periodic solutions of some nonlinear second-order and first-order difference equations. We obtain, in particular upper and lower solutions theorems, Ambrosetti-Prodi type results and sharp existence conditions for nonlinearities which are bounded from below or above.

Document type Article de périodique (Journal article) – Article de recherche
Publication date 2006
Language Anglais
Journal information "Journal of Difference Equations and Applications" - Vol. 12, no. 7, p. 677-695 (2006)
Peer reviewed yes
Publisher Taylor & Francis Ltd (Abingdon)
issn 1023-6198
e-issn 1563-5120
Publication status Publié
Affiliation UCL - SC/MATH - Département de mathématique
Keywords difference equations ; periodic solutions ; Ambrosetti-Prodi conditions ; upper and lower solutions ; Landesman-Lazer conditions
Links
  1. Agarwal R.P., Difference Equations and Inequalities (2000)
  2. Deimling K., Nonlinear Functional Analysis (1985)
  3. Fabry C., Mawhin J., Nkashama M. N., A Multiplicity Result for Periodic Solutions of Forced Nonlinear Second order Ordinary Differential Equations, 10.1112/blms/18.2.173
  4. Henderson Johnny, Thompson H.B., Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations, 10.1080/10236190108808274
  5. Henderson J., Thompson H.B., Existence of multiple solutions for second-order discrete boundary value problems, 10.1016/s0898-1221(02)00095-0
  6. Kelley W.G., Difference Equations (2001)
  7. Mawhin J., Topological Degree Methods in Nonlinear Boundary Value Problems (1979)
  8. Mawhin J., Points Fixes, Points Critiques et Problèmes aux Limites (1985)
  9. Mawhin, J. 1986.Ambrosetti–Prodi Type Results in Nonlinear Boundary Value Problems, Lecture Notes in Mathematics No. 1285 390–413. Berlin: Springer.
  10. Mawhin Jean, A Simple Approach to Brouwer Degree Based on Differential Forms, 10.1515/ans-2004-0409
  11. Mawhin Jean, Thompson ‡b H.B., Tonkes ¶b Elliot, Uniqueness for Boundary Value Problems for Second Order Finite Difference Equations, 10.1080/10236190410001710301
  12. Thompson H.B., Existence of multiple solutions for finite difference approximations to second-order boundary value problems, 10.1016/s0362-546x(02)00297-3
  13. Ward James R., Asymptotic conditions for periodic solutions of ordinary differential equations, 10.1090/s0002-9939-1981-0597653-2
Bibliographic reference Bereanu, Cristian ; Mawhin, Jean. Existence and multiplicity results for periodic solutions of nonlinear difference equations. In: Journal of Difference Equations and Applications, Vol. 12, no. 7, p. 677-695 (2006)
Permanent URL http://hdl.handle.net/2078.1/38263