Finite Morse index solutions of exponential problems
Annales de l'I.H.P. Analyse non linéaire, Volume 25 (2008) no. 1, p. 173-179
@article{AIHPC_2008__25_1_173_0,
author = {Dancer, Edward Norman},
title = {Finite Morse index solutions of exponential problems},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {25},
number = {1},
year = {2008},
pages = {173-179},
doi = {10.1016/j.anihpc.2006.12.001},
zbl = {1136.35030},
mrnumber = {2383085},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2008__25_1_173_0}
}

Dancer, E. N. Finite Morse index solutions of exponential problems. Annales de l'I.H.P. Analyse non linéaire, Volume 25 (2008) no. 1, pp. 173-179. doi : 10.1016/j.anihpc.2006.12.001. http://www.numdam.org/item/AIHPC_2008__25_1_173_0/

[1] Ambrosio L., Cabré X., Entire solutions of semilinear elliptic equations in ${R}^{3}$ and a conjecture of De Giorgi, J. Amer. Math. Soc. 13 (4) (2000) 725-739, (electronic). | MR 1775735 | Zbl 0968.35041

[2] Bahri A., Lions P.-L., Solutions of superlinear elliptic equations and their Morse indices, Comm. Pure Appl. Math. 45 (9) (1992) 1205-1215. | MR 1177482 | Zbl 0801.35026

[3] Bidaut-Véron M.-F., Véron L., Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations, Invent. Math. 106 (3) (1991) 489-539. | MR 1134481 | Zbl 0755.35036

[4] Buffoni B., Dancer E.N., Toland J.F., The sub-harmonic bifurcation of Stokes waves, Arch. Ration. Mech. Anal. 152 (3) (2000) 241-271. | MR 1764946 | Zbl 0962.76012

[5] Chandrasekhar S., An Introduction to the Study of Stellar Structure, University of Chicago Press, Chicago, 1939. | JFM 65.1543.02 | Zbl 0022.19207

[6] Dancer E.N., Stable and not too unstable solutions on ${R}^{n}$ for small diffusion, in: Brunner , Zhao , Zou (Eds.), Nonlinear Dynamics and Evolution Equations, Fields Institute Communications, Amer. Math. Soc., 2006, pp. 67-94. | MR 2223349 | Zbl pre05035632

[7] Dancer E.N., Stable and finite Morse index solutions on ${R}^{n}$ or on bounded domains with small diffusion, Trans. Amer. Math. Soc. 357 (3) (2005) 1225-1243. | MR 2110438 | Zbl 1145.35369

[8] E.N. Dancer, Finite Morse index solutions of supercritical problems, J. Reine Angew. Math., submitted for publication. | MR 2427982 | Zbl 1158.35013

[9] Dancer E.N., Stable solutions on ${R}^{n}$ and the primary branch of some non-self-adjoint convex problems, Differential Integral Equations 17 (9-10) (2004) 961-970. | MR 2082455 | Zbl 1150.35357

[10] Dancer E.N., Infinitely many turning points for some supercritical problems, Ann. Mat. Pura Appl. (4) 178 (2000) 225-233. | MR 1849387 | Zbl 1030.35073

[11] Dancer E.N., Real analyticity and non-degeneracy, Math. Ann. 325 (2) (2003) 369-392. | MR 1962054 | Zbl 1040.35033

[12] Hayman W., Kennedy P., Subharmonic Functions, Academic Press, London, 1979. | Zbl 0419.31001

[13] Joseph D.D., Lundgren T.S., Quasilinear Dirichlet problems driven by positive sources, Arch. Ration. Mech. Anal. 49 (1972/73) 241-269. | MR 340701 | Zbl 0266.34021

[14] Moschini L., New Liouville theorems for linear second order degenerate elliptic equations in divergence form, Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (1) (2005) 11-23. | Numdam | MR 2114409 | Zbl 1130.35070

[15] Saut J.-C., Temam R., Generic properties of nonlinear boundary value problems, Comm. Partial Differential Equations 4 (3) (1979) 293-319. | MR 522714 | Zbl 0462.35016

[16] Suzuki T., Semilinear Elliptic Equations, GAKUTO International Series. Mathematical Sciences and Applications, vol. 3, Gakkōtosho Co. Ltd., Tokyo, 1994. | MR 1428686 | Zbl 0852.35043