Neumann boundary value problems across resonance

Ginés López; Juan-Aurelio Montero-Sánchez

ESAIM: Control, Optimisation and Calculus of Variations (2006)

  • Volume: 12, Issue: 3, page 398-408
  • ISSN: 1292-8119

Abstract

top
We obtain an existence-uniqueness result for a second order Neumann boundary value problem including cases where the nonlinearity possibly crosses several points of resonance. Optimal and Schauder fixed points methods are used to prove this kind of results.

How to cite

top

López, Ginés, and Montero-Sánchez, Juan-Aurelio. "Neumann boundary value problems across resonance." ESAIM: Control, Optimisation and Calculus of Variations 12.3 (2006): 398-408. <http://eudml.org/doc/249678>.

@article{López2006,
abstract = { We obtain an existence-uniqueness result for a second order Neumann boundary value problem including cases where the nonlinearity possibly crosses several points of resonance. Optimal and Schauder fixed points methods are used to prove this kind of results. },
author = {López, Ginés, Montero-Sánchez, Juan-Aurelio},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Second order Newmann boundary condition; resonance; Pontryagin's maximum principle.; Second order Neumann boundary condition; Pontryagin's maximum principle},
language = {eng},
month = {6},
number = {3},
pages = {398-408},
publisher = {EDP Sciences},
title = {Neumann boundary value problems across resonance},
url = {http://eudml.org/doc/249678},
volume = {12},
year = {2006},
}

TY - JOUR
AU - López, Ginés
AU - Montero-Sánchez, Juan-Aurelio
TI - Neumann boundary value problems across resonance
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2006/6//
PB - EDP Sciences
VL - 12
IS - 3
SP - 398
EP - 408
AB - We obtain an existence-uniqueness result for a second order Neumann boundary value problem including cases where the nonlinearity possibly crosses several points of resonance. Optimal and Schauder fixed points methods are used to prove this kind of results.
LA - eng
KW - Second order Newmann boundary condition; resonance; Pontryagin's maximum principle.; Second order Neumann boundary condition; Pontryagin's maximum principle
UR - http://eudml.org/doc/249678
ER -

References

top
  1. B. Beauzamy, Introduction to Banach Spaces and their Geometry. North Holland, New York. Mathematics Studies 68 (1982).  Zbl0491.46014
  2. P. Hartman and A. Wintner, On an oscillation criterion of Liapunoff. Amer. J. Math.73 (1951) 885–890.  Zbl0043.08704
  3. A.C. Lazer and D.E. Leach, On a nonlinear two-point boundary value problem. J. Math. Anal. Appl.26 (1969) 20–27.  Zbl0195.37701
  4. Y. Li and H. Wang, Neumann boundary value problems for second order ordinary differential equations across resonance. SIAM J. Control Optim.33 (1995) 1312–11325.  
  5. J. Mawhin, J.R. Ward and M. Willem, Variational methods and semi-linear elliptic equations. Arch. Rational Mech. Anal.95 (1986) 269–277.  Zbl0656.35044
  6. E.R. Pinch, Optimal Control and the Calculus of Variations. Oxford University Press, New York (1993).  
  7. W. Walter, Ordinary differential equations. Springer-Verlag, New York, Graduate Texts in Math.182 (1998).  Zbl0991.34001

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.