no. 3
Neumann boundary value problems across resonance
ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 398-408.

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.

DOI : 10.1051/cocv:2006009
Classification : 34B15, 47H15
Mots clés : second order Newmann boundary condition, resonance, Pontryagin's maximum principle 
@article{COCV_2006__12_3_398_0,
     author = {L\'opez, Gin\'es and Montero-S\'anchez, Juan-Aurelio},
     title = {Neumann boundary value problems across resonance},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {398--408},
     publisher = {EDP-Sciences},
     volume = {12},
     number = {3},
     year = {2006},
     doi = {10.1051/cocv:2006009},
     mrnumber = {2224820},
     zbl = {1123.34011},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv:2006009/}
}
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
PY  - 2006
SP  - 398
EP  - 408
VL  - 12
IS  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/cocv:2006009/
DO  - 10.1051/cocv:2006009
LA  - en
ID  - COCV_2006__12_3_398_0
ER  - 
%0 Journal Article
%A López, Ginés
%A Montero-Sánchez, Juan-Aurelio
%T Neumann boundary value problems across resonance
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2006
%P 398-408
%V 12
%N 3
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/cocv:2006009/
%R 10.1051/cocv:2006009
%G en
%F COCV_2006__12_3_398_0
López, Ginés; Montero-Sánchez, Juan-Aurelio. Neumann boundary value problems across resonance. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 398-408. doi : 10.1051/cocv:2006009. http://www.numdam.org/articles/10.1051/cocv:2006009/

[1] B. Beauzamy, Introduction to Banach Spaces and their Geometry. North Holland, New York. Mathematics Studies 68 (1982). | MR | Zbl

[2] P. Hartman and A. Wintner, On an oscillation criterion of Liapunoff. Amer. J. Math. 73 (1951) 885-890. | Zbl

[3] A.C. Lazer and D.E. Leach, On a nonlinear two-point boundary value problem. J. Math. Anal. Appl. 26 (1969) 20-27. | Zbl

[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. | Zbl

[5] J. Mawhin, J.R. Ward and M. Willem, Variational methods and semi-linear elliptic equations. Arch. Rational Mech. Anal. 95 (1986) 269-277. | Zbl

[6] E.R. Pinch, Optimal Control and the Calculus of Variations. Oxford University Press, New York (1993). | MR | Zbl

[7] W. Walter, Ordinary differential equations. Springer-Verlag, New York, Graduate Texts in Math. 182 (1998). | MR | Zbl

Cité par Sources :