Singly Periodic Solutions of a Semilinear Equation

Allain, GenevièVe; Beaulieu, Anne

doi:10.1016/j.anihpc.2008.10.001

Allain, GenevièVe ; Beaulieu, Anne

Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1277-1297.

MR Zbl | 1 citation dans Numdam

DOI : 10.1016/j.anihpc.2008.10.001

@article{AIHPC_2009__26_4_1277_0,
     author = {Allain, Genevi\`eVe and Beaulieu, Anne},
     title = {Singly {Periodic} {Solutions} of a {Semilinear} {Equation}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1277--1297},
     publisher = {Elsevier},
     volume = {26},
     number = {4},
     year = {2009},
     doi = {10.1016/j.anihpc.2008.10.001},
     mrnumber = {2542725},
     zbl = {1172.35375},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2008.10.001/}
}

TY  - JOUR
AU  - Allain, GenevièVe
AU  - Beaulieu, Anne
TI  - Singly Periodic Solutions of a Semilinear Equation
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 1277
EP  - 1297
VL  - 26
IS  - 4
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2008.10.001/
DO  - 10.1016/j.anihpc.2008.10.001
LA  - en
ID  - AIHPC_2009__26_4_1277_0
ER  -

%0 Journal Article
%A Allain, GenevièVe
%A Beaulieu, Anne
%T Singly Periodic Solutions of a Semilinear Equation
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 1277-1297
%V 26
%N 4
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2008.10.001/
%R 10.1016/j.anihpc.2008.10.001
%G en
%F AIHPC_2009__26_4_1277_0

Allain, GenevièVe; Beaulieu, Anne. Singly Periodic Solutions of a Semilinear Equation. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1277-1297. doi : 10.1016/j.anihpc.2008.10.001. http://www.numdam.org/articles/10.1016/j.anihpc.2008.10.001/

Bibliographie
Cité par

[1] Adimurthi , Mancini G., Yadava S. L., The Role of Mean Curvature in a Semilinear Neumann Problem Involving the Critical Sobolev Exponent, Comm. Partial Differential Equations 20 (3-4) (1995) 591-631. | MR | Zbl

[2] Allain G., Beaulieu A., High Frequency Periodic Solutions of Semilinear Equations, C. R. Acad. Sci. Paris, Ser. I 345 (2007). | MR | Zbl

[3] Almeida L., Damascelli L., Ge Y., A Few Symmetry Results for Nonlinear Elliptic PDE on Noncompact Manifolds, Ann. Inst. H. Poincaré Anal. Non Linéaire 19 (3) (2002) 313-342. | Numdam | MR | Zbl

[4] Ambrosetti A., Malchiodi A., Ni W. M., Singularly Perturbed Elliptic Equations With Symmetry: Existence of Solutions Concentrating on Spheres II, Indiana Univ. Math. J. 53 (2) (2004) 297-329. | MR | Zbl

[5] Berestycki H., Nirenberg L., On the Method of Moving Plane and the Sliding Method, Bol. Soc. Bras. Mat. 22 (1991) 1-39. | MR | Zbl

[6] Buffoni B., Toland J., Analytic Theory of Global Bifurcation. an Introduction, Princeton Series in Applied Mathematics, Princeton University Press, Princeton, NJ, 2003. | MR | Zbl

[7] Cheng S. Y., Eigenfunctions and Nodal Sets, Comment. Math. Helv. 51 (1976) 43-55. | MR | Zbl

[8] Courant R., Hilbert D., Methods of Mathematical Physics, I, Interscience, 1962. | Zbl

[9] Crandall M., Rabinowitz P., Bifurcation From Simple Eigenvalues, J. Funct. Anal. 8 (1973) 161-180. | MR | Zbl

[10] Dancer E. N., New Solutions of Equations on $R^{n}$ , Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) XXX (2001) 535-563. | Numdam | MR | Zbl

[11] Dancer E. N., Yan S., Multipeak Solutions for a Singularly Perturbed Neumann Problem, Pacific J. Math. 189 (2) (1999) 241-261. | MR | Zbl

[12] Del Pino M., Musso M., Pistoia A., Supercritical Boundary Bubbling in a Semilinear Neumann Problem, Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (1) (2005) 45-82. | Numdam | MR | Zbl

[13] Gidas B., Ni W. M., Nirenberg L., Symmetry of Positive Solutions of Nonlinear Elliptic Equations in $R^{n}$ , in: Mathematical Analysis and Applications, Part a, Adv. Math. Suppl. Studies, vol. 7A, Academic Press, New York, 1981, pp. 369-402. | MR | Zbl

[14] Gilbarg D., Trudinger N., Elliptic Partial Differential Equations of Second Order, second ed., Springer-Verlag, Berlin, 1983. | MR | Zbl

[15] Kwong M. K., Uniqueness of Positive Solutions of $Δ u - u + u^{p} = 0$ in $R^{n}$ , Arch. Rational Mech. Anal. 105 (3) (1989) 243-266. | MR | Zbl

[16] Malchiodi A., Montenegro M., Boundary Concentration Phenomena for a Singularly Perturbed Elliptic Problem, Comm. Pure Appl. Math. LV (2002) 1507-1568. | MR | Zbl

[17] Protter M. H., Weinberger H. F., Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1967. | MR | Zbl

[18] Sattinger D., Topics in Stability and Bifurcation Theory, Lecture Notes in Math., vol. 309, Springer-Verlag, 1973. | MR | Zbl

[19] Rabinowitz P., Some Aspects of Nonlinear Eigenvalue Problems, Rocky Mountain J. Math. 3 (2) (1973) 161-202. | MR | Zbl

[20] Volpert A., Volpert V., Fredholm Property of General Elliptic Problems, Trans. Moscow Math. Soc. (2006) 127-197. | MR

Cité par Sources :