Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 7 (1980) no. 4, pp. 539-603.
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     title = {Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {539--603},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 7},
     number = {4},
     year = {1980},
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     zbl = {0452.47077},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1980_4_7_4_539_0/}
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Amann, H.; Zehnder, E. Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 7 (1980) no. 4, pp. 539-603. http://archive.numdam.org/item/ASNSP_1980_4_7_4_539_0/

[1] S. Ahmad - A.C. Lazer - J.L. Paul, Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Indiana Univ. Math. I., 25 (1976), pp. 933-944. | MR | Zbl

[2] H. Amann, Saddle points and multiple solutions of differential equations, Math. Z., 169 (1979), pp. 127-166. | MR | Zbl

[2a] H. Amann - E. Zehnder, Multiple periodic solutions for a class of nonlinear autonomous wave equations, to appear in Houston J. of Math. | MR | Zbl

[2b] H. Amann - E. Zehnder, Periodic solutions of asymptotically linear Hamiltonian equations, to appear.

[3] A. Ambrosetti - G. Mancini, Theorems of existence and multiplicity for nonlinear elliptic problems with noninvertible linear part, Ann. Scuola Norm. Sup. Pisa, 5 (1978), pp. 15-28. | Numdam | MR | Zbl

[4] A. Ambrosetti - G. Mancini, Existence and multiplicity results for nonlinear elliptic problems with linear part at resonance. The case of the single eigenvalue, J. Differential Equations, 28 (1978), pp. 220-245. | MR | Zbl

[5] A. Ambrosetti - G. Prodi, Analisi non Lineare, Scuola Norm. Sup. Pisa, 1973. | Zbl

[6] A. Ambrosetti - P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Functional Analysis, 14 (1973), pp. 349-381. | MR | Zbl

[7] M. Berger, On a family of periodic solutions of Hamiltonian systems. J. Differential Equations, 10 (1971), pp. 17-26. | MR | Zbl

[8] M. Berger, On periodic solutions of second order Hamiltonian systems, J. Math. Anal. Appl., 29 (1970), pp. 512-522. | MR | Zbl

[9] M. Berger, Periodic solutions of second order dynamical systems and isoperimetric variational problems, Amer. J. Math., 93 (1971), pp. 1-10. | MR | Zbl

[10] D. Blackmore, On local normal forms for diffeomorphisms and flows, Notices Amer. Math. Soc., (1977), A-313.

[11] M. Bottkol, Bifurcation of periodic orbits on manifolds, and Hamiltonian systems. Thesis N.Y.U. (1978). | MR

[12] N. Bourgoyne - R. Cushman, Normal forms for real linear Hamiltonian systems, in Lie Groups : History, Frontiers, and Applications, vol. VII, editors : C. Martin and R. Hermann, Math. Sci. Press, Brookline Mass., 1977, pp. 483-529. | MR

[13] H. Brezis - L. Nirenberg, Forced vibrations for a nonlinear wave equation. Comm. Pure Appl. Math., 31 (1978), pp. 1-30. | MR | Zbl

[14] H. Brezis - L. Nirenberg, Characterizations of the ranges of some nonlinear operators and applications to boundary value problems, Ann. Scuola Norm. Sup. Pisa, Ser. IV, 5 (1978), pp. 225-326. | Numdam | MR | Zbl

[15] A. Castro - A.C. Lazer, Critical point theory and the number of solutions of a nonlinear Dirichlet problem, Ann. Mat. pura e appl., (IV) 120 (1979), pp.113-137. | MR | Zbl

[15a] D.C. Clark, Periodic solutions of variational systems of ordinary differential equations, J. Differential Equations, 28 (1978), pp. 354-368. | MR | Zbl

[16] F.H. Clarke, Periodic solutions to Hamiltonian inclusions, Preprint, Vancouver, 1978. | MR

[17] F.H. Clarke - I. Ekeland, Hamiltonian trajectories having prescribed minimal period, Cahiers de mathématiques de la Decision N. 7822, Université de Paris IX (1978).

[18] C.C. Conley, Isolated invariant sets and the Morse index, CBMS Regional Conference Series in Math., 38 (1978), AMS, Providence, R.I. | MR | Zbl

[19] C.C. Conley - R.W. Easton, Isolated invariant sets and isolating blocks, Trans. Amer. Math. Soc., 158 (1971), pp. 35-61. | MR | Zbl

[20] J.M. Coron, Résolution de l'équation Au + Bu = f où A est linéaire autoadjoint et B déduit d'un potential convexe, C. R. Acad. Sci. Paris Sér. A-B, 288 (1979), pp. A805-A808. | MR | Zbl

[21] I. Ekeland, Periodic solutions of Hamiltonian equations and a theorem of P. Rabinowitz, Cahiers de Mathématiques de la Decison N. 7827, Université de Paris IX (1978). | MR

[22] I. Ekeland - J.-M. Lasry, Nombre de solutions périodiques des équations de Hamilton, Preprint, Paris (1978). | MR

[23] I. Ekeland - R. Temam, Analyse convexe et problèmes variationels, Dunod, Paris (1974). | MR | Zbl

[24] E.R. Fadell - P. Rabinowitz, Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems, Invent. Math., 45 (1978), pp. 139-174. | MR | Zbl

[25] A. Friedman, Partial Differential equations, Holt, Rinehart and Winston, Inc., New York, 1969. | MR | Zbl

[26] P. Hess, Solutions nontriviales d'un problème aux limites elliptique non linéaire, C.R. Acad. Sci. Paris, to appear.

[27] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, New York, 1966. | MR | Zbl

[28] A. Liapunoff, Problème générale de la stabilité du mouvement, Ann. Fac. Sci. Toulouse (2) (1907), pp. 203-474. | JFM | Numdam | MR

[29] J.L. Lions - E. Magenes, Non-Homogeneous Boundary Value Problems and Applications - I, Springer-Verlag, Berlin-Heidelberg -New York, 1972. | Zbl

[30] G. Mancini, Periodic solutions of some semilinear autonomious wave equations, Boll. Un. Mat. Ital., (5), 15-B (1978), pp. 649-672. | MR | Zbl

[31] J. Moser, Periodic orbits near an equilibrium and a theorem by Alan Weinstein, Comm. Pure Appl. Math., 29 (1976), pp. 727-747. | MR | Zbl

[31a] J. Moser, New aspects in the theory of stability of Hamiltonian systems, Comm. Pure Appl. Math., 11 (1958), pp. 81-114. | MR | Zbl

[32] K.J. Palmer, Linearization near an integral manifold, J. Math. Anal. Appl., 51 (1975), pp. 243-255. | MR | Zbl

[33] P. Rabinowitz, Periodic solutions of nonlinear hyperbolic partial differential equations, Comm. Pure Appl. Math., 20 (1967), pp. 145-205. | MR | Zbl

[34] P. Rabinowitz, Some minimax theorems and applications to nonlinear partial differential equations, Nonlinear Analysis, A Collection of Papers in Honor of Erich H. Rothe, pp. 161-177, Academic Press, 1978. | MR | Zbl

[35] P. Rabinowitz, Free vibrations for a semilinear wave equation, Comm. Pure Appl. Math., 31 (1978), pp. 31-68. | MR | Zbl

[36] P. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math., 31 (1978), pp. 157-184. | MR | Zbl

[37] R.T. Rockafellar, Monotone operators associated with saddle-functions and minimax theorems, in Nonlinear Functional Analysis, Part I, Proc. Symp. Pure Math., 18 (1970), pp. 241-250. | MR | Zbl

[38] A.N. Shoshitaishvili, Bifurcations of topological type at singular points of parametrized vector fields, Functional Anal. Appl., 6 (1972), pp. 169-170. | Zbl

[39] C.L. Siegel - J. Moser, Lectures on Celestial Mechanics, Springer-Verlag, New York, 1971. | MR | Zbl

[40] E.H. Spanier, Algebraic Topology, McGraw-Hill Book Co., Inc., New York, 1966. | MR | Zbl

[41] K. Thews, A reduction method for some nonlinear Dirichlet problems, J. Nonlinear Analysis. Theory, Methods, Appl., 3 (1979), pp. 795-813. | MR | Zbl

[42] K. Thews, Nontrivial solutions of elliptic equations at resonance, Proc. Roy. Soc. Edinburgh, 85 A (1980), pp. 119-129. | MR | Zbl

[43] O. Vejvoda, Periodic solutions of nonlinear partial differential equations of evolution, Proc. Symp. Diff. Eqs. Appl. at Bratislava, 1966, Acta Fac. Rerum Natur. Univ. Comenian. Math., 17 (1967), pp. 293-300. | MR | Zbl

[44] A. Weinstein, Periodic orbits for convex Hamiltonian systems, Ann. of Math., 108 (1978), pp. 507-518. | MR | Zbl

[45] A. Weinstein, Bifurcations and Hamilton's principle, Math. Z., 159 (1978), pp. 235-248. | MR | Zbl

[46] A. Weinstein, Normal modes for nonlinear Hamiltonian systems, Invent. Math., 20 (1973), pp. 47-57. | MR | Zbl

[47] A. Weinstein, Lagrangian submanifolds and Hamiltonian systems, Ann. of Math., 98 (1973), pp. 377-410. | MR | Zbl

[48] G.W. Whitehead, Elements of Homotopy Theory, Springer-Verlag, New York, Heidelberg, Berlin, 1978. | MR | Zbl

[49] J. Williams, On the algebraic problem concerning the normal form of a linear dynamical system, Amer. J. Math., 58 (1936), pp. 141-163. | JFM | MR