Multi-bump type nodal solutions having a prescribed number of nodal domains : I
Annales de l'I.H.P. Analyse non linéaire, Volume 22 (2005) no. 5, p. 597-608
@article{AIHPC_2005__22_5_597_0,
     author = {Liu, Zhaoli and Wang, Zhi-Qiang},
     title = {Multi-bump type nodal solutions having a prescribed number of nodal domains : I},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {22},
     number = {5},
     year = {2005},
     pages = {597-608},
     doi = {10.1016/j.anihpc.2004.10.002},
     zbl = {1130.35054},
     zbl = {02235970},
     mrnumber = {2171993},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2005__22_5_597_0}
}
Liu, Zhaoli; Wang, Zhi-Qiang. Multi-bump type nodal solutions having a prescribed number of nodal domains : I. Annales de l'I.H.P. Analyse non linéaire, Volume 22 (2005) no. 5, pp. 597-608. doi : 10.1016/j.anihpc.2004.10.002. http://www.numdam.org/item/AIHPC_2005__22_5_597_0/

[1] N. Ackermann, T. Weth, Multibump solutions to nonlinear periodic Schrödinger equations in a degenerate setting, Comm. Contemp. Math., submitted for publication. | MR 2151860 | Zbl 1070.35083

[2] Bartsch T., Critical point theory on partially ordered Hilbert spaces, J. Funct. Anal. 186 (2001) 117-152. | MR 1863294 | Zbl 1211.58003 | Zbl 01679364

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

[4] Bartsch T., Liu Z.L., Weth T., Sign changing solutions of superlinear Schrödinger equations, Comm. Partial Differential Equations 29 (2004) 25-42. | MR 2038142 | Zbl 1140.35410 | 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] Brezis H., Nirenberg L., H 1 versus C 1 local minimizers, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993) 465-472. | MR 1239032 | Zbl 0803.35029

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

[8] 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

[9] Chang K.C., H 1 versus C 1 isolated critical points, C. R. Acad. Sci. Paris Sér. I Math. 319 (1994) 441-446. | MR 1296769 | Zbl 0810.35025

[10] Coti Zelati V., Rabinowitz P.H., Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, J. Amer. Math. Soc. 4 (1991) 627-693. | MR 1119200 | Zbl 0744.34045

[11] Coti Zelati V., Rabinowitz P.H., Homoclinic type solutions for a semilinear elliptic PDE on R n , Comm. Pure Appl. Math. 45 (1992) 1217-1269. | MR 1181725 | Zbl 0785.35029

[12] Dancer E.N., Du Y., On sign-changing solutions of certain semilinear elliptic problems, Appl. Anal. 56 (1995) 193-206. | MR 1383886 | Zbl 0835.35051

[13] Dancer E.N., Yan S., A singularly perturbed elliptic problem in bounded domains with nontrivial topology, Adv. Differential Equations 4 (1999) 347-368. | MR 1671254 | Zbl 0947.35075

[14] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of the Second Order, Springer-Verlag, Berlin, 1983. | MR 737190 | Zbl 0562.35001

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

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

[17] Liu Z.L., Sun J.X., Invariant sets of descending flow in critical point theory with applications to nonlinear differential equations, J. Differential Equations 172 (2001) 257-299. | MR 1829631 | Zbl 0995.58006

[18] Liu Z.L., Wang Z.-Q., Multi-bump type nodal solutions having a prescribed number of nodal domains: II, Ann. I. H. Poincaré - AN 22 (2005) 609-631. | Numdam | MR 2171994 | Zbl 02235971

[19] Rabinowitz P.H., Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conf. Ser. in Math., vol. 65, Amer. Math. Soc., Providence, RI, 1986. | MR 845785 | Zbl 0609.58002

[20] Rabinowitz P.H., A variational approach to multibump solutions of differential equations, in: Contemp. Math., vol. 198, Amer. Math. Soc., Providence, RI, 1996, pp. 31-43. | MR 1409152 | Zbl 0874.58019

[21] Rabinowitz P.H., Multibump solutions of differential equations: an overview, Chinese J. Math. 24 (1996) 1-36. | MR 1399183 | Zbl 0968.37019

[22] Séré E., Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Z. 209 (1992) 27-42. | MR 1143210 | Zbl 0725.58017