Hostname: page-component-5cf477f64f-54txb Total loading time: 0 Render date: 2025-04-05T17:52:38.381Z Has data issue: false hasContentIssue false
  • English
  • Français

Neumann boundary value problemsacross resonance

Published online by Cambridge University Press:  20 June 2006

Ginés López  and
Juan-Aurelio Montero-Sánchez
Ginés López
Affiliation:
Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain; glopezp@ugr.es;jmontero@ugr.es
Juan-Aurelio Montero-Sánchez
Affiliation:
Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain; glopezp@ugr.es;jmontero@ugr.es
Get access

Abstract

We obtain an existence-uniqueness result fora second order Neumann boundary value problem including caseswhere the nonlinearity possibly crosses several points ofresonance. Optimal and Schauder fixed points methods are used toprove this kind of results.

Keywords

Second order Newmann boundary conditionresonancePontryagin's maximum principle.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 3 , July 2006 , pp. 398 - 408
Copyright
© EDP Sciences, SMAI, 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

B. Beauzamy, Introduction to Banach Spaces and their Geometry. North Holland, New York. Mathematics Studies 68 (1982).
Hartman, P. and Wintner, A., On an oscillation criterion of Liapunoff. Amer. J. Math. 73 (1951) 885–890. CrossRef
Lazer, A.C. and Leach, D.E., On a nonlinear two-point boundary value problem. J. Math. Anal. Appl. 26 (1969) 20–27. CrossRef
Li, Y. and Wang, H., Neumann boundary value problems for second order ordinary differential equations across resonance. SIAM J. Control Optim. 33 (1995) 1312–11325. CrossRef
Mawhin, J., Ward, J.R. and Willem, M., Variational methods and semi-linear elliptic equations. Arch. Rational Mech. Anal. 95 (1986) 269–277. CrossRef
E.R. Pinch, Optimal Control and the Calculus of Variations. Oxford University Press, New York (1993).
W. Walter, Ordinary differential equations. Springer-Verlag, New York, Graduate Texts in Math. 182 (1998).