Minimax characterization of solutions for a semi-linear elliptic equation with lack of compactness
Buffoni, Boris ; Jeanjean, Louis
Annales de l'I.H.P. Analyse non linéaire, Tome 10 (1993), p. 377-404 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_1993__10_4_377_0,
     author = {Buffoni, Boris and Jeanjean, Louis},
     title = {Minimax characterization of solutions for a semi-linear elliptic equation with lack of compactness},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {10},
     year = {1993},
     pages = {377-404},
     mrnumber = {1246458},
     zbl = {0828.35013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1993__10_4_377_0}
}

Buffoni, Boris; Jeanjean, Louis. Minimax characterization of solutions for a semi-linear elliptic equation with lack of compactness. Annales de l'I.H.P. Analyse non linéaire, Tome 10 (1993) pp. 377-404. http://gdmltest.u-ga.fr/item/AIHPC_1993__10_4_377_0/

[1] S. Alama and Y.Y. Li, Existence of Solutions for Semilinear Elliptic Equations with Indefinite Linear Part, J. Diff. Eqns., 96, 1992, pp. 89-115. | MR 1153310 | Zbl 0766.35009

[2] J.P. Aubin, L'analyse nonlinéaire et ses motivations économiques, Masson, Paris, 1984. | MR 754997 | Zbl 0551.90001

[3] V. Benci, Critical Point Theory for Strongly Indefinite Functionals with Symmetries, Trans. A.M.S., 274, 1982. | MR 675067 | Zbl 0504.58014

[4] V. Benci and P.H. Rabinowitz, Critical Point Theorems for Indefinite Functions, Invent. Math., Vol. 52, 1979, pp. 241-273. | MR 537061 | Zbl 0465.49006

[5] B. Buffoni and L. Jeanjean, Bifurcation from the Spectrum Towards Regular Value, to appear in J. Reine Angew. Math. | MR 1244967 | Zbl 0795.47041

[6] S.N. Chow and J.K. Hale, Methods of Bifurcation Theory, Springer, Berlin, 1982. | MR 660633 | Zbl 0487.47039

[7] H.P. Heinz, Lacunary Bifurcation for Operator Equations and Nonlinear Boundary Value Problems on RN, Proceedings of the Royal Society of Edinburgh, 118 A, 237-270, 1991. | MR 1121666 | Zbl 0765.47017

[8] H.P. Heinz, Existence and Gap-Bifurcation of Multiple Solutions to Certain Nonlinear Eigenvalue Problems, preprint. | MR 1240897

[9] H.P. Heinz, T. Kupper and C.A. Stuart, Existence and Bifurcation of Solutions for Nonlinear Perturbations of the Periodic Schrödinger Equation, J. Diff. Eqns., Vol. 100, 2, 1992, pp. 341-354. | MR 1194814 | Zbl 0767.35006

[10] H.P. Heinz and C.A. Stuart, Solvability of Nonlinear Equation in Spectral Gaps of the Linearisation, Nonlinear Analysis - TMA, Vol. 19, 2, 1992, pp. 145-165. | MR 1174464 | Zbl 0777.47033

[11] T. Kupper and C.A. Stuart, Bifurcation Into Gaps in the Essential Spectrum, J. Reine Angew. Math., Vol. 409, 1990, pp. 1-34. | MR 1061517 | Zbl 0709.34507

[12] T. Kupper and C.A. Stuart, Necessary and Sufficient Conditions for Gap-Bifurcation, Nonlinear Analysis, Vol. 18, 1992, pp. 893-903. | MR 1162481 | Zbl 0797.47037

[13] T. Kupper and C.A. Stuart, Gap-Bifurcation for Nonlinear Perturbations of Hill's Equation, J. Reine Angew. Math., Vol. 410, 1990, pp. 23-52. | MR 1068798 | Zbl 0704.34012

[14] P.L. Lions, The Concentration-Compactness Principle in the Calculus of Variations, Part 1, Ann. Inst. H. Poincaré, Anal. non lin., Vol. 1, 1984, pp. 109-145. | Numdam | MR 778970 | Zbl 0541.49009

[15] P.L. Lions, The Concentration-Compactness Principle in the Calculus of Variations, Part 2, Ann. Inst. H. Poincaré, Anal. non lin., Vol. 1, 1984, pp. 223-283. | Numdam | MR 778974 | Zbl 0704.49004

[16] P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS conference lectures, A.M.S., Providence, 1986. | MR 845785 | Zbl 0609.58002

[17] H.J. Ruppen, The Existence of Infinitely Many Bifurcation Branches, Proc. Roy. Soc. Edinbourgh, Vol. 101, 1985, pp. 307-320. | MR 824229 | Zbl 0603.35006

[18] H. Ruppen, Nodal Characterisation of Bifurcating Branches in Lp (R) for a Semilinear Equation, J. Diff. Eqns., Vol. 99, 1, 1992, pp. 153-203. | MR 1178401 | Zbl 0767.34057

[19] C.A. Stuart, Bifurcation from the Continuous Spectrum in L2-Theory of Elliptic Equations on RN, in Recent Methods in Nonlinear Analysis and Applications, Liguori, Napoli, 1981. | Zbl 0614.47047

[20] C.A. Stuart, Bifurcation for Dirichlet Problems Without Eigenvalues, Proc. London Math. Meth. Soc., Vol. 45, 1982, pp. 169-192. | MR 662670 | Zbl 0505.35010

[21] C.A. Stuart, Bifurcation in Lp (RN) for a Semilinear Elliptic Equation, Proc. London Math. Meth. Soc., (3), Vol. 57, 1988, pp. 511-541. | MR 960098 | Zbl 0673.35005

[22] C.A. Stuart, Bifurcation from the Essential Spectrum for Some Non-Compact Nonlinearities, Math. in the applied sciences, Vol. 11, 1989, pp. 525-542. | MR 1001101 | Zbl 0678.58013

[23] X.P. Zhu and H.S. Zhou, Bifurcation from the Essential Spectrum of Superlinear Elliptic Equations, Appl. Anal., Vol. 28, 1988, pp. 51-66. | MR 960586 | Zbl 0621.35009