A variational approach to bifurcation into spectral gaps
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 28 (1999) no. 4, p. 651-674
@article{ASNSP_1999_4_28_4_651_0,
     author = {Giacomoni, Jacques and Jeanjean, Louis},
     title = {A variational approach to bifurcation into spectral gaps},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 28},
     number = {4},
     year = {1999},
     pages = {651-674},
     zbl = {0961.35032},
     mrnumber = {1760535},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1999_4_28_4_651_0}
}
Giacomoni, Jacques; Jeanjean, Louis. A variational approach to bifurcation into spectral gaps. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 28 (1999) no. 4, pp. 651-674. http://www.numdam.org/item/ASNSP_1999_4_28_4_651_0/

[1] S. Alama - Y.Y. Li, Existence of solutions for semilinear elliptic equations with indefinite linear part, J. Differential Equations 96 (1992), 89-115. | MR 1153310 | Zbl 0766.35009

[2] V. Benci - P.H. Rabinowitz, Critical point theorems for indefinite functions, Invent. Math. 52 (1979), 241-273. | MR 537061 | Zbl 0465.49006

[3] H. Brezis - J.M. Coron - L. Nirenberg, Free vibrations for a nonlinear wave equation and a theorem of P. H. Rabinowitz, Comm. Pure Appl. Math. 33 (1980), 667-689. | MR 586417 | Zbl 0484.35057

[4] H. Brezis - L. Nirenberg, Remarks on finding critical points, Comm. Pure Appl. Math. 44 (1991), 939-963. | MR 1127041 | Zbl 0751.58006

[5] B. Buffoni, "Un problème variationnel fortement indéfini sans compacité", Ph. D. Thesis, EPFL, Lausanne, 1992.

[6] B. Buffoni - L. Jeanjean, Bifurcation from the essential spectrum towards regular values, J. Reine Angew. Math. 445 (1993), 1-29. | MR 1244967 | Zbl 0795.47041

[7] B. Buffoni - L. Jeanjean, Minimax characterisation of solutions for a semi-linear elliptic equation with lack of compactness, Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (1993), 377-404. | Numdam | MR 1246458 | Zbl 0828.35013

[8] B. Buffoni - L. Jeanjean - C.A. Stuart, Existence of a nontrivial solution to a strongly indefinite semilinear equation, Proc. Amer. Math. Soc. 119 (1993), 179-186. | MR 1145940 | Zbl 0789.35052

[9] V. Coti-Zelati - I. Ekeland - E. Séré, A variational approach to homoclinic orbits in Hamiltonian systems, Math. Ann. 288 (1990), 133-160. | MR 1070929 | Zbl 0731.34050

[10] M.J. Esteban - E. Séré, Stationnary states of the nonlinear Dirac equation: a variational approach, Comm. Math. Phys. 171 (1995), 323-350. | MR 1344729 | Zbl 0843.35114

[11] H.-P. Heinz, Bifurcation from the essential spectrum for nonlinear pertubations of Hill's equation, In "Differential Equations-Stability and Control " S. ELAYDI (ed.), Marcel Dekker, New York, 1990, pp. 219-226. | Zbl 0723.35008

[12] H.-P. Heinz, Lacunary bifurcation for operator equations and nonlinear boundary value problems on RN, Proc. Roy. Soc. Edinburgh Sect. A 118 (1991), 237-270. | MR 1121666 | Zbl 0765.47017

[13] H.-P. Heinz - C.A. Stuart, Solvability of nonlinear equations in spectral gaps of the linearisation, Nonlinear Anal. 19 (1992), 145-165. | MR 1174464 | Zbl 0777.47033

[14] H.-P. Heinz - T. Küpper - C.A. Stuart, Existence and bifurcation of solutions for nonlinear pertubations of the periodic Schrödinger equation, J. Differential Equations 100 (1992), 341-354. | MR 1194814 | Zbl 0767.35006

[15] H. Hofer - K. Wysocki, First order elliptic system and the existence of homoclinic orbits in Hamiltonian systems, Math. Ann. 288 (1990), 483-503. | MR 1079873 | Zbl 0702.34039

[16] T. Küpper - C.A. Stuart, Bifurcation into gaps in the essential spectrum, J. Reine Angew. Math. 409 (1990), 1-34. | MR 1061517 | Zbl 0697.47063

[17] R. Joosten, Bifurcation of homoclinic solutions for Hamiltonian systems, in preparation.

[18] L. Jeanjean, Solution in spectral gaps for a nonlinear equation of Schrödinger type, J. Differential Equations 112 (1994), 53-80. | MR 1287552 | Zbl 0804.35033

[19] L. Jeanjean, "Approche minimax des solutions d'une équation semi-linéaire elliptique en l'absence de compacité", Ph. D. Thesis, EPFL, Lausanne, 1992.

[20] L. Jeanjean, On the existence of bounded Palais-Smale sequences and application to a Landesman-Lazer type problem set on RN, Proc. Roy. Soc. Edinburgh, to appear. | Zbl 0935.35044

[21] L. Jeanjean, Local conditions insuring bifurcation from the continuous spectrum, Math. Z., to appear. | MR 1727546 | Zbl 0934.35047

[22] L. Jeanjean - J.F. Toland, Bounded Palais-Smale mountain-pass sequences, C. R. Acad. Sci. Paris Sér. I Math. 327 (1998), 23-28. | MR 1650239 | Zbl 0996.47052

[23] W. Kryszewski - A. Szulkin, Generalized linking theorem with an application to a semilinear Schrödinger equation, Adv. Differential Equations 3 (1998), 441-472. | MR 1751952 | Zbl 0947.35061

[24] M. Struwe, "Variational Methods", Springer, Second Edition, 1996. | MR 1411681 | Zbl 0864.49001

[25] C.A. Stuart, "Bifurcation into spectral gaps", Société Mathématique de Belgique, 1995. | MR 1361485 | Zbl 0864.47037

[26] C. Troestler, Bifurcation into spectral gaps for a noncompact semilinear Schrödinger equation with nonconvex potential, Preprint.

[27] C. Troestler - M. Willem, Nontrivial solution of a semilinear Schrödinger equation, Comm. Partial Differential Equations 21 (1996), 1431-1449. | MR 1410836 | Zbl 0864.35036

[28] M. Willem, "Minimax Theorems", Birkhaüser, Boston, 1996. | MR 1400007 | Zbl 0856.49001