Solutions of minimal period of a wave equation via a generalization of a Hofer's theorem

 Access to full text

 Full (PDF)

1. [1] A. Ambrosetti - G. MANCINI, Solutions of minimal period for a class of convex Hamiltonian systems, Math. Ann., 155 (1981). Zbl0466.70022MR615860
2. [2] A. Ambrosetti - P. H. RABINOWITZ, Dual variational methods in a critical point theory and applications, J. Funct. Anal., 14 (1973), pp. 345-381. Zbl0273.49063MR370183
3. [3] P. Bartolo - V. BENCI - D. FORTUNATO: Abstract critical point theorems and applications to some nonlinear problems with « strong » resonance at infinity, Nonlinear Anal., T.M.A., 7 (1983), pp. 981-1012. Zbl0522.58012MR713209
4. [4] V. Benci, Some applications of the generalized Morse-Conley index, Conferenze del Seminario di Matematica dell'Università di Bari, 217 (1987). Zbl0656.58006MR898735
5. [5] V. Benci - D. FORTUNATO, The dual method in critical point theory. Multiplicity results for indefinite functionals, Ann. Mat. Pura Appl., 32 (1981), pp. 215-242. Zbl0526.58013MR696044
6. [6] V. Benci - D. FORTUNATO, Subharmonic solutions of prescribed minimal period for non autonomous differential equations, Edited by G. F. DELL'ANTONIO - B. D'ONOFRIO, World Scientific, Singapore (1987), pp. 83-96. Zbl0663.70028MR902625
7. [7] H. Brezis, Periodic solutions of nonlinear vibrating strings and duality principles, Bull. Amer. Math. Soc., 3 (1983), pp. 409-426. Zbl0515.35060MR693957
8. [8] H. Brezis - J.M. Coron - L. Nirenberg, Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz, Comm. Pure Appl. Math., 33 (1980), pp. 667-689. Zbl0484.35057MR586417
9. [9] J.M. Coron, Periodic solution of a nonlinear wave without assumptions of monotonicity, Math. Ann., 252 (1983), pp. 273-285. Zbl0489.35061MR690201
10. [10] D. Gromoll - W. MEYER, On differentiable functions with isolated critical points, Topology, 8 (1969), pp. 361-369. Zbl0212.28903MR246329
11. [11] H. Hofer, A note on the topological degree at a critical point of mountain pass-type, Proc. Amer. Math. Soc., 90, 2 (1984), pp. 309-315. Zbl0545.58015MR727256
12. [12] H. Hofer, A geometric description of the neighbourhood of a critical point given by the mountain-pass theorem, J. London Math. Soc., 31 (1985), pp. 566-570. Zbl0573.58007MR812787
13. [13] H. Lovicarova, Periodic solutions of a weakly nonlinear wave equation in one dimensional, Czech. Math. J., 19 (1969), pp. 324-342. Zbl0181.10901MR247249
14. [14] P.H. Rabinowitz, Variational Methods for Nonlinear Eigenvalue Problems, Edited by G. PRODI, Edizione Cremonese, Roma (1974), pp. 141-195. MR464299
15. [15] P. Rockafeller, Convex Analysis, Princeton University Press (1970). Zbl0193.18401MR274683
16. [16] A. Salvatore, Solutions of minimal period for a semilinear wave equation, to appear on Ann. Mat. Pura e Appl. Zbl0714.35052MR1042839
17. [17] G. Tarantello, Solutions with prescribed minimal period for nonlinear vibrating strings, Comm. P.D.E., 12, 9 (1987), pp. 1071-1094. Zbl0628.35007MR888007