Three nodal solutions of singularly perturbed elliptic equations on domains without topology
Bartsch, Thomas ; Weth, Tobias
Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005), p. 259-281 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_2005__22_3_259_0,
     author = {Bartsch, Thomas and Weth, Tobias},
     title = {Three nodal solutions of singularly perturbed elliptic equations on domains without topology},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {22},
     year = {2005},
     pages = {259-281},
     doi = {10.1016/j.anihpc.2004.07.005},
     mrnumber = {2136244},
     zbl = {02192472},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2005__22_3_259_0}
}

Bartsch, Thomas; Weth, Tobias. Three nodal solutions of singularly perturbed elliptic equations on domains without topology. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) pp. 259-281. doi : 10.1016/j.anihpc.2004.07.005. http://gdmltest.u-ga.fr/item/AIHPC_2005__22_3_259_0/

[1] Ambrosetti A., Rabinowitz P.H., Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973) 349-381. | MR 370183 | Zbl 0273.49063

[2] Bartsch T., Critical point theory on partially ordered Hilbert spaces, J. Funct. Anal. 186 (2001) 117-152. | MR 1863294 | Zbl 01679364

[3] Bartsch T., Chang K.-C., Wang Z.-Q., On the Morse indices of sign changing solutions of nonlinear elliptic problems, Math. Z. 233 (2000) 655-677. | MR 1759266 | Zbl 0946.35023

[4] Bartsch T., Liu Z., Weth T., Sign changing solutions to superlinear Schrödinger equations, Comm. Partial Differential Equations 29 (2004) 25-42. | MR 2038142 | Zbl 02130224

[5] Bartsch T., Wang Z.-Q., On the existence of sign changing solutions for semilinear Dirichlet problems, Topol. Methods Nonlinear Anal. 7 (1996) 115-131. | MR 1422008 | Zbl 0903.58004

[6] Bartsch T., Weth T., A note on additional properties of sign changing solutions to superlinear Schrödinger equations, Topol. Methods Nonlinear Anal. 22 (2003) 1-14. | MR 2037264 | Zbl 1094.35041

[7] Benci V., Cerami G., Positive solutions of semilinear elliptic problems in exterior domains, Arch. Rational Mech. Anal. 99 (1987) 283-300. | MR 898712 | Zbl 0635.35036

[8] Benci V., Cerami G., Multiple positive solutions of some elliptic problems via the Morse theory and the domain topology, Calc. Var. 2 (1994) 29-48. | MR 1384393 | Zbl 0822.35046

[9] Cao D., Noussair E.S., Multi-peak solutions for a singularly perturbed semilinear elliptic problem, J. Differential Equations 166 (2000) 266-289. | MR 1781257 | Zbl 0966.35039

[10] Castro A., Cossio J., Neuberger J.M., A sign-changing solution for a superlinear Dirichlet problem, Rocky Mountain J. Math. 27 (1997) 1041-1053. | MR 1627654 | Zbl 0907.35050

[11] Castro A., Cossio J., Neuberger J.M., A minmax principle, index of the critical point, and existence of sign-changing solutions to elliptic BVPs, Electronic J. Differential Equations 2 (1998) 18. | Zbl 0901.35028

[12] Chabrowski J., Weak Convergence Methods for Semilinear Elliptic Equations, World Scientific, River Edge, NJ, 1999. | MR 1885519 | Zbl 1059.35038

[13] Chang K.C., Infinite Dimensional Morse Theory and Multiple Solution Problems, Progr. Nonlinear Differential Equations Appl., vol. 6, Birkhäuser, Boston, 1993. | MR 1196690 | Zbl 0779.58005

[14] Conti M., Terracini S., Verzini G., Nehari's problem and competing species systems, Ann. Inst. H. Poincaré Anal. Non Linéaire 19 (2002) 871-888. | Numdam | MR 1939088 | Zbl 1090.35076

[15] Coti-Zelati V., Rabinowitz P.H., Homoclinic type solutions for a semilinear elliptic PDE on R N , Comm. Pure Appl. Math. XLV (1992) 1217-1269. | MR 1181725 | Zbl 0785.35029

[16] Deimling K., Ordinary differential equations in Banach spaces, in: Lecture Notes in Math., vol. 596, Springer, Berlin, 1978. | MR 463601 | Zbl 0361.34050

[17] Gidas B., Ni W., Nirenberg L., Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979) 209-243. | MR 544879 | Zbl 0425.35020

[18] Li S.J., Wang Z.-Q., Mountain pass theorems in order intervals and multiple solutions for semilinear elliptic Dirichlet problems, J. Anal. Math. 81 (2000) 373-396. | MR 1785289 | Zbl 0962.35065

[19] Li S.J., Wang Z.-Q., Lusternik-Schnirelman theory in partially ordered Hilbert spaces, Trans. Amer. Math. Soc. 354 (2002) 3207-3227. | MR 1897397 | Zbl 01738053

[20] Li Y., Nirenberg L., The Dirichlet problem for singularly perturbed elliptic equations, Comm. Pure Appl. Math. 51 (1998) 1445-1490. | MR 1639159 | Zbl 0933.35083

[21] Lions P., Symétrie et compacité dans les espaces de Sobolev, J. Funct. Anal. 49 (1982) 315-334. | MR 683027 | Zbl 0501.46032

[22] Lions P., The concentration-compactness principle in the calculus of variations. The locally compact case. Part II, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984) 223-283. | Numdam | MR 778974 | Zbl 0704.49004

[23] Müller-Pfeiffer E., On the number of nodal domains for eigenfunctions of elliptic differential operators, J. London Math. Soc. (2) 31 (1985) 91-100. | MR 810566 | Zbl 0579.35063

[24] Struwe M., Multiple solutions of differential equations without the Palais-Smale condition, Math. Ann. 261 (1982) 399-412. | MR 679798 | Zbl 0506.35034

[25] Struwe M., Variational Methods, Springer, Berlin, 1990. | MR 1078018 | Zbl 0746.49010

[26] Wang Z.-Q., On a superlinear elliptic equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (1991) 43-57. | Numdam | MR 1094651 | Zbl 0733.35043