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Critical point theorems for indefinite functionals. (English) Zbl 0465.49006

MSC:
49J35Minimax problems (existence)
49J27Optimal control problems in abstract spaces (existence)
49L99Hamilton-Jacobi theories, including dynamic programming
34C25Periodic solutions of ODE
70H99Hamiltonian and Lagrangian mechanics
References:
[1]Rabinowitz, P.H.: Free vibrations for a semilinear wave equation. Comm. Pure Appl. Math.31, 31-68 (1978) · doi:10.1002/cpa.3160310103
[2]Rabinowitz, P.H.: Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math.31, 157-184 (1978) · Zbl 0369.70017 · doi:10.1002/cpa.3160310203
[3]Rabinowitz, P.H.: A variational method for finding periodic solutions of differential equations, Nonlinear Evolution Equations (M.G. Grandall, ed.) pp. 225-251. New York: Academic Press, 1978
[4]Rabinowitz, P.H.: Periodic solutions of a Hamiltonian system on a prescribed energy surface, J. Diff. Eq. in press
[5]Krasnoselski, M.A.: Topological Methods in the Theory of Nonlinear Integral Equations, New York: Macmillan, 1964
[6]Ambrosetti, A., Rabinowitz, P.H.: Dual variational methods in critical point theory and applications, J. Functional Analysis,14, 349-381 (1973) · Zbl 0273.49063 · doi:10.1016/0022-1236(73)90051-7
[7]Rabinowitz, P.H.: Variational methods for nonlinear eigenvalue problems, Eigenvalues of Nonlinear Problems (G. Prodi, ed.) pp. 141-195. Roma: Edizion Cremonese, 1974
[8]Rabinowitz, P.H.: Some critical point theorems and applications to semilinear elliptic partial differential equations, Ann. Scuol. Norm. Sup. Pisa, Ser IV, Vol. 11, 215-223 (1978)
[9]Benci, V.: Some critical point theorems and applications, in press
[10]Rabinowitz, P.H.: Some minimax theorems and applications to nonlinear partial differential equations, Nonlinear analysis (Cesari, Kannan, and Weinberger, ed.) pp. 161-177. New York: Academic Press, 1978
[11]Ahmad, S., Lazer, A.C., Paul, J.L.: Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Ind. Univ. Math. J.,25, 933-944 (1976) · Zbl 0351.35036 · doi:10.1512/iumj.1976.25.25074
[12]Lazer, A.C., Landesman, E.M., Meyers, D.R.: On saddle point problems in the calculus of variations, the Ritz algorithm, and monotone convergence, J. Math. Anal. and Appl.52, 594-614 (1975) · Zbl 0354.35004 · doi:10.1016/0022-247X(75)90084-0
[13]Castro, A., Lazer, A.C.: Applications of a maximin principle, preprint
[14]Zygmund, A.: Trignometric Series, New York: Cambridge University Press, 1959
[15]Lax, P.D.: On Cauchy’s problem for hyperbolic equations and the differentiability of solutions of elliptic equations, Comm. Pure Appl. Math.8, 615-633 (1955) · Zbl 0067.07502 · doi:10.1002/cpa.3160080411
[16]Clarke, F.H., Ekeland, I.: Hamiltonian trajectories having prescribed minimal period, Preprint
[17]Brezis, H., Nirenberg, L.: Forced vibrations of a nonlinear wave equation, Comm. Pure Appl. Math.,31, 1-31 (1978) · Zbl 0378.35040 · doi:10.1002/cpa.3160310102